Discard any fat from the cavity of the capon but keep the neck (reserve the giblets for another use). Let stand at room temperature for 30 minutes. Meanwhile, finely chop enough of the onions, celery and bell pepper to measure 3 tbsp. each. In a heavy, medium skillet, cook the vegetables with 1 tbsp. butter and a pinch salt over medium heat, stirring occasionally, until golden, about 10 minutes. Remove the skillet from the heat; stir in the garlic, tomato paste and cayenne. Let the vegetables cool slightly, then stir in the remaining 7 tbsp. butter.
Position a rack in the middle of the oven; preheat to 400°. Put the capon in a roasting pan along with the neck. Gently loosen the skin by sliding your fingers between the skin and flesh of the breast. Push the butter mixture evenly under the skin on both sides of the breast, then massage the skin to distribute. Tuck the wings under and sprinkle the cavity of the capon with 1/2 tsp. salt. Quarter 1 onion and 1 celery rib and place them in the cavity. Cut the remaining onion, celery and bell pepper into 1-inch chunks and scatter them around the capon. Tie the legs together; sprinkle the capon with 1 tsp. salt.
Roast the capon for 30 minutes. Lower the oven temperature to 375°; baste every 20 minutes. Roast until an instant-read thermometer inserted into a thigh away from the bone registers 170°, 1 hour more. (Tent with foil if it browns too quickly.)
Tilt the roasting pan so that the juices run out of the cavity. Transfer the capon to a cutting board and let stand, uncovered, for 20 to 30 minutes. Pour the pan juices through a sieve into a measuring cup. Skim off and reserve any fat.
Add enough broth to the pan juices in the measuring cup to equal 2 cups. In a heavy, medium saucepan, cook the flour in 2 tbsp. of the reserved fat over medium heat, stirring constantly, until golden, about 5 minutes. Add 2 cups of the broth mixture, then boil gently, stirring occasionally, until the sauce is reduced to 1 1/2 cups, about 12 minutes. Season with salt and pepper. Carve; serve with the sauce.