Heat 2 tablespoons olive oil in a large pot or Dutch oven over medium-high heat until shimmering.
Add the finely chopped carrots, green and red bell peppers, and diced onion; cook 3–4 minutes until they begin to soften.
Add the ground turkey to the pot and cook, breaking it up with a spoon, until browned and cooked through.
Stir in crushed tomatoes, tomato sauce, tomato paste, minced garlic, dried oregano, dried basil (or Italian seasoning), sea salt, cracked pepper, and red pepper if using.
Reduce heat to medium-low and simmer, partially covered, about 30 minutes until the vegetables are tender and the sauce has thickened, stirring occasionally.
Taste and adjust seasoning as needed, then serve over pasta.