Bake the hash-brown patties at 425°F for 18 to 20 minutes, turning once, until deep golden and crisp.
Cook the bacon in a skillet over medium heat until crisp, then drain it on a rack.
Pour off all but 1 teaspoon bacon fat and toast the brioche buns cut-side down for 1 minute.
Fry the eggs over-medium in the skillet, season with salt and black pepper, and cook until they reach 160°F.
Top each egg with cheddar and cover for 30 seconds.
Build each bun with one hash brown, two bacon slices and one cheesy egg.