Heat oil in a large nonstick skillet over medium heat. Add sausage and cook, breaking up clumps with a spoon, until browned, about 3 minutes. Add onion and carrot and cook, stirring frequently, until vegetables soften and begin to brown, about 4 minutes. Add garlic, oregano and crushed red pepper; cook, stirring, for 1 minute more. Stir in wine and increase heat to high. Cook, stirring occasionally, until wine has evaporated, about 5 minutes. Add tomatoes and roasted red peppers; reduce heat to low. Cover and simmer, stirring often, until sauce is thickened, about 30 minutes. Add broth and return to a simmer.