Roast the red peppers (if not using jarred).
Place whole red bell peppers under the broiler or over a gas flame, turning until skins are blackened. Transfer to a bowl, cover, and let steam for 10 minutes. Peel, remove seeds, and roughly chop.
Sauté the aromatics.
Warm olive oil in a large pot over medium heat. Add onion with a pinch of salt and cook 5–7 minutes until soft and translucent. Stir in garlic and cook 30 seconds until fragrant.
Build the heat and aroma.
Add chili flakes (or fresh chili) and smoked paprika. Stir for 30 seconds to bloom the spices. Adjust the amount of chili now if you want a bolder soup.
Add tomatoes and peppers.
Pour in crushed tomatoes and the chopped roasted red peppers. Stir to combine and scrape up any browned bits from the pot.
Thin and season. Add 3 cups of broth to start and drop in the bay leaf.
Season with salt and pepper. If your tomatoes taste sharp, add the sugar or honey.
Simmer. Bring to a gentle simmer.
Cook 15–20 minutes, stirring occasionally. The flavors will round out, and the soup will slightly thicken.
Blend until smooth. Remove the bay leaf.
Use an immersion blender directly in the pot until silky. Or carefully blend in batches in a countertop blender. Add extra broth if you prefer a thinner texture.
Finish with richness.
Stir in cream or coconut milk, if using. Start with 2 tablespoons and add more to taste. This softens the heat and adds a velvety finish.
Brighten.
Off the heat, add red wine vinegar or lemon juice. Taste and adjust salt, pepper, and chili. A splash of acid at the end makes the flavors pop.
Serve.
Ladle into bowls. Top with chopped basil or parsley, a swirl of yogurt or cream, croutons, and a drizzle of chili oil if you like it extra spicy.