In a heavy-bottomed pot with a lid, warm the olive oil over medium heat. When the oil shimmers, toss in the onion and carrots. Sprinkle with 1 teaspoon kosher salt and black pepper to taste. Sauté, stirring now and then, until the veggies begin to soften, about 5-6 minutes. Mix in the garlic, tomato paste, and red pepper flakes if using. Continue cooking for another 1-2 minutes until the paste darkens and the garlic is aromatic.
Stir in the basil, thyme, crushed tomatoes, vegetable broth, and wine (if using). Combine thoroughly. Bring the soup to a boil, then lower the heat to keep it at a gentle simmer. Partially cover and let it cook for 15 minutes, until the vegetables are fully tender.
In batches, ladle the soup into a stand blender, never filling more than ⅔ full. Take out the center cap from the lid and cover the opening with a thick towel. Blend until silky smooth, then pour back into the pot. Alternatively, use an immersion blender directly in the pot for a smoother process.
Add the cream or your chosen milk, and heat over medium-low, stirring occasionally, until hot. Taste and adjust the seasoning as needed.
Portion the soup into bowls and garnish with cracked pepper, extra red pepper flakes, and fresh basil if desired. Pair with crusty bread or a Gooey Mozzarella Grilled Cheese Sandwich. Enjoy!