Heat olive oil in a heavy-bottomed pot or Dutch oven over medium heat. Add diced onion and carrots. Season with salt and pepper. Cook for 5-6 minutes until vegetables soften. Stir in garlic, tomato paste, and crushed red pepper flakes (if using), cooking for an additional 1-2 minutes until lightly browned.

Add fresh basil, thyme, crushed tomatoes, vegetable broth, and white wine (if using). Stir to combine, then bring to a boil. Reduce heat to a gentle simmer, partially cover, and simmer for 15 minutes until vegetables are tender.

Carefully transfer the soup in batches to a stand blender, filling no more than two-thirds full. Remove the blender lid center cap and cover with a kitchen towel to vent while blending. Blend until smooth. Alternatively, use an immersion blender directly in the pot. Return blended soup to the pot.

Stir in cream, milk, or dairy-free milk substitute. Cook over medium-low heat, stirring occasionally, until warmed through. Adjust salt and pepper to taste.

Ladle soup into bowls and garnish with black pepper, extra crushed red pepper flakes, and fresh basil leaves if desired. Serve with crusty bread or a grilled cheese sandwich.