Bring 1 cup water to a boil. Place sun-dried tomatoes in a bowl and add water. Let stand 10 minutes.
Meanwhile, crumble sausage into a large nonstick skillet. Cook over medium to medium-high heat for 6 minutes. Add peppers and cook, stirring occasionally, 4 minutes. Remove from heat. Drain sun-dried tomatoes and chop. Stir into sausage mixture in skillet.
Place bread cubes in a very large bowl. In a medium bowl, whisk eggs, milk and chopped basil. Stir sausage mixture into bread along with 1 cup of the cheese. Pour egg mixture over bread mixture and stir to moisten all ingredients. Coat a 13 x 9 x 2-inch baking dish with nonstick cooking spray. Pour bread mixture into prepared dish. Cover with plastic wrap and refrigerate overnight.
Heat oven to 350° F. Uncover dish and sprinkle with remaining 1 cup cheese. Cover dish with foil. Bake, covered, at 350° F for 45 minutes. Uncover and bake 15 minutes. Cool slightly before serving.