1. Roast the poblanos

Place the peppers on a broiler-safe baking sheet. Broil, turning with tongs, until blistered and charred on all sides. The exact time depends on the broiler and the distance from the heat.

Watch closely rather than leaving the peppers unattended. A few blackened patches are expected on the skins; avoid burning the flesh until it is brittle.

Transfer to a bowl and cover for about ten minutes. This steam rest loosens the skins and makes peeling easier.

2. Peel, seed, and divide

When cool enough to handle, rub or peel away the loose skins. Remove the stems and seed clusters.

Cut two peppers into short, bite-sized strips. Reserve the other two for blending. Short strips are easier to eat with the noodles than long, unbroken ribbons of pepper.

Avoid rinsing away all the roasted juices unless necessary to remove stubborn skin. A few small flecks of char are fine, but remove loose, heavily burnt skin that could make the broth bitter.

3. Blend the creamy base

Place the two reserved peppers in the blender with the cream, softened cream cheese, and half cup of cool or lukewarm broth. Blend until smooth, scraping down as needed.

The mixture should be creamy and evenly green. If a few tiny pepper pieces remain, they are less important than avoiding large cream-cheese lumps.

Set the base aside briefly while cooking, or refrigerate if preparation will be delayed. Do not leave the dairy mixture sitting out throughout a long make-ahead session.

4. Sauté the onion and spices

Heat the olive oil in the soup pot over medium heat. Add the diced onion and cook about four to five minutes, stirring, until softened.

Add the garlic, cumin, Mexican oregano, and smoked paprika. Stir for about 30 seconds, just until fragrant.

If the garlic begins browning quickly, lower the heat. The spices need only a brief warm-up before the broth is added.

5. Simmer the chicken

Pour in the five cups of broth. Add the chicken, black pepper, and part of the salt if needed. Bring to a gentle simmer, then reduce the heat and partially cover.

Begin checking after about 18 minutes, allowing longer for thick pieces. Maintain a gentle simmer rather than a rolling boil.

Check the thickest part of each large piece for 165°F. Remove cooked pieces as they finish if their sizes differ considerably.

6. Shred and return

Transfer the chicken to a clean cutting board or plate and shred into manageable strands with two forks. Return it to the broth with the sliced poblanos.

If the broth has reduced noticeably, add a splash of extra broth before finishing. Remember that noodles will absorb more liquid if they are cooked directly in the pot.

7. Prepare the rice noodles

For the recommended separate method, cook or soak the noodles according to their package directions while the chicken simmers. Drain and keep ready for prompt serving.

Divide the noodles among bowls instead of leaving them in a large hot mass where they can stick together. If preparing ahead, follow the package’s cooling guidance and refrigerate promptly.

For the direct-in-pot method, add the noodles to the broth before the dairy. Cook only as directed for that product, stirring gently to separate them. Stop when just tender, since they continue softening in the hot soup.

8. Incorporate the creamy base

Reduce the heat to low. Stir in the blended poblano mixture gradually.

Warm gently until the soup is hot throughout, stirring to keep the dairy from catching on the bottom. Avoid a hard boil. If the base was refrigerated, allow enough gentle heating time rather than compensating with very high heat.

If the soup looks thicker than desired, add a little extra broth. Make the adjustment before adding all the cheese so you can judge the final richness more easily.

9. Melt the Monterey Jack

Take the pot off the heat or keep it at the lowest setting. Add the one cup of shredded Monterey Jack in small handfuls, stirring until each melts before adding the next.

Do not dump the cheese into rapidly boiling liquid. Excess heat can encourage clumping, oil separation, or a grainy texture.

The goal is a creamy broth with melted cheese incorporated throughout. A little cheese stretch is possible; avoid promising a perfectly emulsified queso sauce from ordinary melting cheese alone.

10. Taste and assemble bowls

Taste the finished soup and adjust the salt and black pepper. Add extra broth if needed.

If the noodles were prepared separately, ladle the chicken and poblano broth over the noodles in each bowl. Sprinkle the reserved half cup of Monterey Jack across the servings, then add optional queso fresco and cilantro.

Serve lime wedges separately so each person can add a little brightness. A large amount of acidic juice stirred into a hot dairy pot can affect texture, so individual additions are easier to control.