In a bowl, beat egg whites and oil to blend. In another bowl, mix crumbs and chili powder.
Rinse mushroom caps; drain. Coat each cap with egg mixture, drain briefly, then coat with crumbs, shaking off excess. Set caps, gill sides down, slightly apart on a 12- by 15-inch baking sheet. Lay bun halves, cut sides up, side by side on another 12- by 15-inch baking sheet.
Bake mushroom caps in a 450° oven until browned and flexible when pressed, about 20 minutes. About 3 minutes before mushrooms are done, add buns to oven; bake until lightly toasted.
In a small bowl, mix sour cream and chipotle chilies. Spread mixture on cut sides of buns. Layer equal amounts of onion and spinach on each bun bottom, top with a mushroom cap, add salt and pepper to taste, and cover with bun top.