Position a rack in the middle of the oven and preheat to 350 degrees F. Grease a 9-by-13-inch baking dish (glass or ceramic) with nonstick spray; set aside.
Blend the cottage cheese, navy beans, paprika, eggs, scallions, ¾ teaspoon salt and a few cracks of pepper in a high-powered blender on medium-low speed until just smooth.
Pour into the prepared baking dish, cover with foil and bake until the center is set and the edges are puffed, 35 to 40 minutes.
Let cool on a wire rack until cool enough to handle, about 15 minutes (the edges will come down as it cools).
Cut the egg bake into 12 pieces.
Place 1 egg square on the bottom half of an English muffin, then top with a slice of cheese and 2 bacon halves. Top with the other half of the English muffin.
Repeat with the remaining egg squares, English muffins, cheese and bacon. Eat immediately or freeze for later.
Freezing and reheating instructions: Wrap each breakfast sandwich in parchment to enclose completely, then wrap in foil. Store the sandwiches in an airtight container or freezer bag and freeze.
When ready to eat, remove the foil and microwave each parchment-wrapped sandwich on high, turning over halfway, until warmed through, about 2 minutes. Let sit in the microwave undisturbed for 1 minute. If not hot, microwave in 20 second increments until desired temperature.
