Heat the butter in a large skillet over medium heat. Add the onions and cook until they start to turn translucent, about 2-3 minutes. Add the carrots and continue to cook for 1-2 minutes, stir them around so they cook evenly.
Transfer the cooked veggies into a 6 quart slow cooker or larger. Add the tomato sauce, tomatoes, roasted garlic, sun-dried tomatoes, sugar, dried basil, italian seasoning, broth, parmesan rind, bay leaf, basil pesto, and balsamic vinegar. Cover and cook on the low setting for 6-8 hours for the best flavor or 3-4 on the high setting for a quicker meal.
Fish out the bay leaf and parmesan rind. Add the basil leaves to the slow cooker, stir to combine and using an immersion blender, blend the soup till smooth or to your desired consistency. If you don’t have a stick blender, transfer the soup in batches into a blender and blend. Stir in 1 cup of half and half and taste. If desired add more half and half to preference. We like it with 1 cup but you can certainly add more to your preference.
Top bowls with parmesan cheese and serve with grilled cheese or cheese croutons.