Heat oil in large skillet over medium high heat. Add sausage and cook until well-browned. Add onions, bell peppers, and green onions and saute until soft, 3 to 4 minutes. Add chicken broth and cook, stirring, for one minute. Remove skillet from heat.
Place bread cubes in large mixing bowl. Add milk and half and half and stir. Allow to set until milk is completely absorbed, about 10 minutes.
Add onion, peppers, and sausage mixture to bread. Fold in beaten eggs, cheeses, and seasonings. Spoon mixture into buttered 9 x 13" casserole. Can be made ahead and refrigerated overnight at this point. Remove from frig and allow to warm up on counter for 30 minutes before baking. Cover with foil and bake for 50 minutes. Remove foil and bake an additional 20 minutes. Increase oven temperature to 350 degrees. Spread sour cream over top of casserole and sprinkle with Parmesan cheese. Bake uncovered for additional 15 minutes, or until browned on top.