In a 3-quart saucepan, heat the olive oil over medium heat. Add the onion, carrot, celery, garlic, and basil. Cover loosely and cook until the vegetables are softened but not browned, 6 to 8 minutes. Stir in the roasted red pepper, wine, tomato paste, tomatoes, salt and pepper. Bring to a boil, then reduce heat and simmer for 35 to 40 minutes, loosely covered. Uncover and simmer for 15 to 20 minutes longer to thicken. Turn off heat and let stand 5 minutes.
Insert the hand blender into the saucepan, making sure the protective guard is submerged. Blend on Low, using an up-and-down motion until ingredients are well combined, about 30 to 60 seconds, until the sauce reaches desired consistency.