In a skillet over medium heat, add one tablespoon of olive oil. Heat until the oil shimmers.
Add the breakfast sausage meat without any casing. Using two forks and both hands, break the sausage meat apart to get small bite-size pieces. Sauté sausage until it is well browned. Once browned, remove the sausage from the skillet and set aside.
In the same skillet, add the diced onions and peppers. Season with a pinch of salt and black pepper. Cook for about 10 minutes or until onions and peppers are tender. Turn the heat off the skillet.
In a buttered 9x13 baking dish or similar, place one layer of bread on the bottom of the baking dish. Add half of the browned sausage meat on top of the first layer of bread.
Top the sausage meat with half of the onion and pepper mixture then top layer with ¼ cup of shredded cheese. Repeat to make a second layer.
In a large glass jar, combine the milk with the eggs. Shake until combined. You can also use a mixing cup or something with a spout to make pouring easier.
Slowly, pour the milk and egg mixture evenly over the top of the strata. Cover the strata and place in the refrigerator overnight.
In the morning, remove the strata from the refrigerator and preheat the oven to 350 degrees.
Place covered strata in the oven and bake for 45 minutes or until the strata rises and is golden brown. Depending on your oven you may need to bake longer.
Let rest for five minutes before serving.