1. Roast the peppers

Broil or flame-roast the poblanos, turning until their skins are blistered and charred. Watch closely and use tongs appropriate for the heat source.

Transfer to a bowl and cover for about ten minutes. Once cool enough to handle, peel away loose skins and remove stems and seeds.

Dice three peppers into bite-sized pieces. Reserve the fourth for the blender. Wash hands after handling peppers and avoid touching your eyes.

2. Set aside the blending broth

Measure five cups chicken broth in total. Reserve half a cup for the creamy base and keep 4 1/2 cups for the pot.

This small organizing step avoids accidentally using five cups in the pot and adding another half cup without recognizing the change. Extra broth can still be added later if the stew needs it.

3. Blend the creamy base

Blend the reserved pepper with heavy cream, softened cream cheese, and the half cup broth until smooth. Use cool or lukewarm pepper and broth and follow the blender’s instructions.

Scrape down the sides if needed. There should not be large cream cheese lumps or whole pieces of pepper left in the mixture.

Keep the base refrigerated if preparation will be delayed. If you are proceeding directly, set it aside briefly while the chicken cooks, within ordinary safe handling limits.

4. Sauté the aromatics

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

Stir in garlic, cumin, Mexican oregano, and smoked paprika. Cook about 30 seconds until fragrant, lowering the heat if the garlic begins to darken quickly.

The spices need a brief warm-up, not a prolonged dry fry that risks scorching them.

5. Simmer the chicken

Add the remaining 4 1/2 cups broth, chicken, black pepper, and part of the salt if needed. Bring to a gentle simmer, reduce the heat, and cover partially.

Begin checking after about 18 minutes and continue until the thickest part of the chicken reaches 165°F. The exact time depends on the pieces.

A gentle simmer is enough. A rolling boil can reduce the broth unnecessarily and make chicken breasts less tender.

6. Shred and return

Transfer the chicken to a clean plate or cutting board and shred with two forks. Return it to the pot.

If you prefer to keep cooked breast meat out while the shells cook, hold it briefly and return it before the dairy so it warms through without extra simmering. Keep handling time short and safe.

7. Add shells and vegetables

Stir in the dry pasta shells, diced roasted poblanos, corn, and drained tomatoes. Maintain a steady gentle simmer, uncovered.

Stir occasionally, reaching the bottom of the pot so pasta does not settle and stick. Avoid vigorous stirring that breaks tender shells.

Cook according to the pasta package, checking early. Stop when the shells are just tender, since they continue softening in the hot stew.

8. Check the liquid before adding dairy

The pasta may absorb more liquid than expected. If the mixture looks too dry to stir comfortably, add a little warm broth.

The stew should remain loose enough for the creamy base to blend through. Do not let pasta sit against a nearly dry hot bottom while you prepare the next step.

Adding broth gradually preserves the rich flavor better than diluting the pot heavily at the end.

9. Warm the creamy base gently

Reduce the heat to low and stir in the blended poblano mixture. Warm gently, scraping the bottom as you stir.

Avoid bringing the dairy mixture to a hard boil. If it was refrigerated, allow enough gentle heating time rather than turning the burner high to rush it.

The broth should become creamy and lightly green, with visible vegetables and shells throughout.

10. Melt in the cheeses

Remove the pot from the heat or keep it on the lowest setting. Add Monterey Jack in small handfuls, stirring until each melts before adding more. Follow with the cheddar or Oaxaca.

Do not add all the cheese at once to rapidly boiling liquid. Excess heat and large clumps make it harder to obtain an even texture.

If the stew becomes too thick, add a little warm broth. Stop heating once the cheese is melted and the stew is ready to serve.

11. Taste and serve

Taste the finished broth before adding the rest of the salt. The cheeses and broth may already supply enough.

Ladle promptly into bowls. Offer cilantro, avocado, queso fresco, jalapeños, and lime separately so each person can adjust the finish.

A little lime in an individual bowl can brighten the rich sauce. Avoid pouring a large amount of acidic juice into the hot dairy pot, where it can affect texture.