Preheat the oven to 400ยบ F. Coat 4 (1/2 cup) ramekins or coffee cups with cooking spray and set on a baking sheet.
In a large bowl, whisk the eggs, egg whites, squash puree, cheese, flour, baking powder and salt until combined. Divide the mixture among the remekins or cups and bake until the tops are puffed up and the eggs are no longer runny in the center when pierced with the tip of a knife, 13 to 15 minutes. Serve immediately.