Add the butter and onions to a large skillet over medium heat and saute until starting to soften, 3 to 4 minutes. Sprinkle the flour over the onions and whisk them together. Continue cooking the onion/flour mixture until golden brown, about 2 minutes. Stir in the half-and-half and milk and whisk around, allowing the mixture to thicken; this will take 3 to 4 minutes. Add some pepper, stir the sauce, reduce the heat and keep warm.