Heat olive oil in a heavy-bottomed pot or Dutch oven over medium heat. Once hot, add diced onion and carrots. Season with 1 teaspoon kosher salt and ground black pepper to taste. Cook for 5-6 minutes until vegetables become slightly softened. Stir in garlic, tomato paste, and crushed red pepper flakes if using, cooking for an additional 1-2 minutes until the tomato paste browns lightly and garlic is fragrant.

Add fresh basil, thyme, crushed tomatoes, vegetable broth, and white wine (if using) to the pot, stirring to combine. Bring the mixture to a boil, then reduce heat to maintain a gentle simmer. Partially cover with lid and simmer for 15 minutes, until the vegetables are fully tender and flavors meld.

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 the opening with a thick kitchen towel to vent while blending. Blend until smooth and creamy. Alternatively, use an immersion blender in the pot to purée until smooth. Return blended soup to the pot.

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

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