In a large heavy-bottomed pot or Dutch oven, melt 3 tablespoons butter over medium heat. Add the chopped onion, carrot, and celery with a pinch of salt. Cook, stirring occasionally, until softened and translucent, about 8–10 minutes. Add the minced garlic in the last 1 minute and stir until fragrant.

Build flavor

Stir in the tomato paste and cook 2–3 minutes, stirring, until it darkens slightly. Sprinkle the flour over the vegetables and cook, stirring constantly, 1–2 minutes to eliminate the raw flour taste.

Deglaze

Pour in the white wine and scrape any browned bits from the bottom of the pot. Simmer until the wine has mostly evaporated, about 2–3 minutes.

Add liquids

Add the drained chopped tomatoes and roasted red peppers (if using) to the pot. Stir to combine, then pour in the stock. Bring the mixture to a gentle boil, then reduce heat to maintain a simmer.

Simmer

Simmer uncovered for 20–25 minutes to meld flavors and soften vegetables and tomatoes. Taste and add 1 teaspoon salt and 1/2 teaspoon pepper now, adjusting later as needed.

Puree & Finish

Blend until smooth

Working in batches, carefully transfer the hot soup to a blender and puree until very smooth (or use an immersion blender directly in the pot). Return blended soup to the pot and strain through a fine-mesh sieve if an extra-silky texture is desired, pressing solids with the back of a ladle.

Cream and milk

With the pot over low heat, stir in the whole milk and heavy cream until incorporated and warmed through. Heat gently—do not boil after adding dairy—to avoid curdling, about 5 minutes.

Adjust seasoning & finish

Stir in 1 tablespoon butter, 1 teaspoon lemon juice, the remaining 1/2 teaspoon salt (or to taste), and remaining 1/2 teaspoon freshly ground black pepper (or to taste). Taste and adjust acidity with an additional 1/2–1 teaspoon lemon juice or a pinch of sugar if the tomatoes are too acidic.

Serve & Garnish

Ladle the bisque into warm bowls. Garnish each serving with a drizzle of extra-virgin olive oil or a little cream, a sprinkle of fresh basil and chives, and a crack of black pepper. Serve with crusty bread or grilled cheese if desired.