Heat the oven to 350°F with a rack in the middle. Line an 8.5-by-4.5-inch metal loaf pan with oven-safe parchment rated for this temperature, covering the bottom and sides and leaving lifting handles. Drain and rinse the commercially canned white kidney beans. Let excess liquid drip away, then weigh 480 g. Do not include canning liquid in that weight.

Process the beans in a food processor until they form a thick puree, stopping to scrape the bowl and blade area as needed. Add the eggs and process just until smooth and evenly blended. Small flecks of bean skin are fine, but break down any whole beans. Do not taste the raw mixture. Wash hands and food-contact equipment after handling raw eggs.

Transfer the puree to a bowl. Fold in the oat flour until no dry pockets remain, scraping across the bottom. The mixture should be a thick, spoonable batter that holds soft ridges, rather than a kneadable dough. Scrape it into the lined pan, press gently into the corners, and level the surface. Bake promptly; there is no proofing or bench rest.

Bake for 60 minutes, checking at 50 minutes. The top should look dry and lightly golden, the edges should feel firm, and a thermometer inserted into the center should read 200°F. Verify that center temperature before removing this egg-containing loaf. If necessary, continue baking until the center reaches the stated target; oven differences can extend the estimated baking time.

Cool in the pan on a wire rack for 10 minutes. Carefully lift out the loaf using both parchment handles, supporting its bottom with a wide spatula. Ease away the parchment and cool directly on the rack for 50 minutes. Cut into 8 portions and refrigerate promptly. In surroundings above 90°F, finish cooling in the refrigerator rather than on the counter.