Prep the slow cooker base: Add crushed tomatoes, sun-dried tomatoes, onion, garlic, oregano, basil, thyme, red pepper flakes, salt, black pepper, and chicken broth to the slow cooker. Stir to combine.
Season the chicken: Pat the chicken dry and season both sides with a pinch of salt and pepper.
Nestle the pieces into the sauce in an even layer.
Drizzle with olive oil: Pour the olive oil over the top to help carry flavor and keep the chicken moist.
Slow cook: Cover and cook on Low for 4–5 hours or on High for 2–3 hours, until the chicken is tender and reaches 165°F internally. Thighs may need a little longer than breasts.
Shred or slice: Remove the chicken to a plate. Shred with two forks or slice into thick pieces, then return it to the slow cooker.
Make it creamy: Stir in the cream cheese until melted and smooth.
Pour in the heavy cream and mix well. Add Parmesan and stir until the sauce is creamy and cohesive.
Add extras (optional): If using spinach or mushrooms, stir them in now. Cover and cook on Low for 10–15 more minutes, just until the greens wilt or mushrooms soften.
Taste and adjust: Taste the sauce.
Add more salt, pepper, or red pepper flakes if needed. If it’s too tangy, a pinch of erythritol or monk fruit sweetener can balance the acidity without adding carbs.
Serve: Spoon the chicken and sauce over zucchini noodles, spaghetti squash, or cauliflower rice. Finish with fresh basil or parsley and extra Parmesan.