If needed, add remaining EVOO to reserved skillet over medium-high heat. Stir in the carrot, celery, and onion; season with salt. Cook until softened, 4 to 5 minutes. Add the mushrooms, garlic, rosemary, and crushed red pepper; stir, then add tomato paste and stir again. Pour in wine and cook until reduced to 1/3 cup, 2 to 3 minutes (mixture will thicken and you will see a trail when a spoon is moved through it). Add mushroom broth and tomatoes. Return chicken to skillet. Simmer for 5 minutes. Remove skillet to trivet and serve from pan with charred bread.