Roast the peppers: Place bell peppers on a baking tray and broil until the skins are charred, turning occasionally (about 10 minutes).
Cool and peel: Transfer peppers to a covered bowl to steam. Peel off the charred skin and remove seeds.
Sauté garlic: Heat olive oil in a saucepan over medium heat. Add garlic and cook for 30 seconds until fragrant.
Combine ingredients: Add roasted peppers, tomato paste, salt, black pepper, red pepper flakes, smoked paprika, sugar, and balsamic vinegar.
Blend: Transfer the mixture to a blender and blend until smooth.
Simmer: Return the sauce to the saucepan and cook over low heat for 10 minutes to thicken slightly.
Serve or store: Use immediately or store in an airtight container in the fridge for up to a week.