Set the crockpot to high. In a skillet or directly in the crockpot if using a model that allows stovetop-style sauté, melt the butter and stir in the flour; cook, stirring, for 3–5 minutes until combined and slightly roux-like.
Add the chopped onion, garlic, Italian seasoning, and chili flakes to the butter-flour mixture and cook until the onion is softened, about 3–4 minutes.
Stir in the chopped celery, drained sun-dried tomatoes, and broth. Season with salt and black pepper to taste.
Cover and cook in the crockpot on low for 4–6 hours or on high for 1–2 hours. (If using a stovetop method, simmer covered for about 15 minutes.)
During the final 15–20 minutes of cooking on high, stir in the pasta, chopped spinach, heavy cream, and milk. Cover and cook on high until the pasta is tender (about 15–20 minutes in the crockpot or about 8 minutes if added to boiling soup on the stove).
Stir in the shredded provolone and grated parmesan until melted and incorporated. If the soup is too thick, thin with additional broth or water to your desired consistency.
Adjust seasoning with salt and pepper, then serve warm.
