Prep the base. Add crushed tomatoes, tomato paste, chopped onion, minced garlic, Italian seasoning, red pepper flakes (if using), chicken broth, olive oil, and 1/2 teaspoon salt to the crockpot. Stir to combine.
Nestle in the chicken. Place chicken breasts or thighs into the sauce.
Spoon some sauce over the top. Season with a pinch more salt and pepper.
Cook low and slow. Cover and cook on Low for 4–6 hours or High for 2.5–3.5 hours, until the chicken is cooked through and fork-tender.
Add the creaminess. Stir in heavy cream or softened cream cheese until the sauce turns silky and rich. Taste and adjust salt and pepper.
Finish with basil. Stir in most of the chopped fresh basil, saving a little for garnish.
The fresh herbs brighten the sauce.
Shred or slice. Shred chicken directly in the crockpot with two forks, or remove and slice. Return to the sauce and stir to coat.
Serve. Spoon over pasta, rice, mashed potatoes, or zucchini noodles. Top with extra basil and grated Parmesan if you like.