Step 1

Preheat the oven to 350 degrees F (175 degrees C).

Step 2

Cut each roll into 8 cubes. Spread onto a baking sheet in a single layer.

Step 3

Bake in the preheated oven until toasted, about 10 minutes.

Step 4

Layer toasted bread cubes in a 1 1/2-quart baking pan. Sprinkle 1/4 cup Swiss cheese, 1/4 cup Cheddar cheese, 1/2 the bacon, and 2 green onions on top of the bread. Shake to settle the toppings into the bread.

Step 5

Beat eggs together with half-and-half, milk, salt, and pepper in a bowl. Pour over the bread cubes, pressing cubes down into the mixture. Sprinkle the remaining Swiss cheese, Cheddar cheese, bacon, green onions, and Parmesan cheese on top.

Step 6

Bake in the preheated oven until strata is hot in the center, about 30 minutes.