Butter a 13x9 baking dish. Whisk first 7 ingredients together in a large bowl. Set aside.
Place bread cubes in a large bowl.
Warm olive oil in large saute pan over medium heat. Add the breakfast sausage links and brown 4 minutes each side. Remove sausage from pan to a plate and cut into chunks. To the same saute pan add the red peppers and onions and continue to saute for 7-9 minutes. Remove from the heat.
Pour the egg mixture over the bread cubes. Add the sausage, peppers and onion mixture and 1 1/2 cups of the shredded cheese. Stir until blended. Transfer to prepared baking dish. Press the mixture down with a spatula to thoroughly soak everything. Cover bake with plastic wrap and refrigerate for at least 2 hours, preferably overnight.
Preheat oven to 375 degrees. Sprinkle bake with remaining 1/2 cup shredded cheese. Bake uncovered until puffy and golden brown, about 45 minutes. Let stand 10 minutes before serving.