Sauté the Aromatics: In a large skillet over medium heat, melt the butter. Add the chopped onions and sauté until they become translucent and fragrant (about 3 minutes). Stir in the diced carrots and cook for another 2 minutes to soften them slightly.
Fill the Slow Cooker: Transfer the sautéed onions and carrots into a 6-quart or larger slow cooker. Add the San Marzano tomatoes (break them up slightly with a spoon), tomato sauce, roasted garlic, sun-dried tomatoes, and broth.
Season and Simmer: Add the sugar, basil pesto, balsamic vinegar, dried basil, Italian seasoning, the bay leaf, and the parmesan rind. Stir to combine.
Slow Cook: Cover and cook on Low for 6–8 hours (recommended for the deepest flavor) or High for 3–4 hours.
Blend to Perfection: Once the time is up, remove and discard the bay leaf and the parmesan rind. Add the fresh basil leaves to the pot. Use an immersion blender to blend the soup directly in the slow cooker until it reaches your desired smoothness. (If using a standard blender, work in small batches and be careful with the hot liquid).
The Creamy Finish: Stir in the half and half. Start with one cup, taste, and add more if you prefer a richer, creamier soup.
Serve: Ladle into bowls and top with plenty of freshly grated parmesan cheese. Serve immediately with a buttery grilled cheese sandwich for dipping.