Rinse the peppers and cut them in half lengthwise. Remove and discard stems, seeds, and veins. Lay peppers, cut sides down, in a 10- by 15-inch pan. Broil 4 to 6 inches from heat until skins are blackened all over, about 12 minutes. When the peppers are cool enough to handle, pull off and discard skins; chop peppers.
In a 3- to 4-quart pan over medium-high heat, stir onion in butter until limp, about 3 minutes. Stir in peppers and carrots.
Add flour and stir about 1 minute. Add broth, half-and-half, and tomato sauce; stir until mixture boils and is slightly thickened, about 10 minutes.
Stir in chili flakes and salt and pepper to taste.