Heat the oven to 400°F with a rack in the middle. Line a 13-by-18-inch rimmed baking sheet with parchment rated for this oven temperature. Mark a 9-by-12-inch rectangle on the underside as a spreading guide. Rinse the fully cooked Great Northern beans, drain thoroughly, then weigh 300 g. Let excess moisture drip away before weighing; use the drained beans rather than their packing liquid.

Put the drained beans in a food processor. Add the eggs and process until creamy, stopping to scrape the bowl and underside of the blade as needed. Small flecks of bean skin are fine, but crush any visible bean pieces. Add the oat flour and pulse just until evenly incorporated. The mixture should resemble thick, spreadable hummus and hold a soft ridge from a spatula. Do not taste the raw batter. Wash hands and food-contact equipment after handling raw eggs.

Scrape the batter onto the prepared parchment. Spread it evenly inside the rectangle, approximately 1/4 inch thick, using a flexible spatula. Keep the center and edges at similar thickness, and round off thin corners so they do not dry out ahead of the middle. Do not leave a mound in the center. Move directly to baking; this batter needs no resting or proofing.

Bake for 30 minutes at 400°F. Begin checking at 25 minutes: the surface should look matte, the edges lightly golden, and the center firm under gentle pressure. Insert a food thermometer sideways into the center to check doneness. If the middle remains wet, continue baking until it is set. Confirm the safe internal temperature specified below before serving.

Confirm that the center has reached an internal temperature of 165°F before cooling. Cool on the baking sheet for 5 minutes, then carefully slide the parchment and flatbread onto a wire rack for 10 minutes. Peel the parchment away gently and cut into 4 equal rectangles. Serve warm, or refrigerate promptly according to the storage directions.