Preheat your oven to 450°F (230°C). Cut the peppers in half lengthwise and remove seeds and membranes. Place them cut-side down on a baking sheet lined with parchment paper, brush with olive oil, and roast for 20-25 minutes until the skins are charred and blistered.
Transfer the hot peppers to a bowl and cover with plastic wrap or a kitchen towel. Let them steam for 10-15 minutes to loosen the skins. Once cooled slightly, gently peel away the charred skin. Don't rinse the peppers under water as this washes away the valuable smoky flavor.
Heat 2 tablespoons of olive oil in a medium saucepan over medium heat. Add the minced garlic, chopped shallot, and red pepper flakes. Sauté for 2-3 minutes until fragrant and translucent but not browned.
Add the peeled roasted peppers, tomato paste, and broth to the pan with the aromatics. Simmer for 5-7 minutes to marry the flavors. Transfer the mixture to a blender or food processor, add the remaining tablespoon of olive oil and herbs, then process until smooth. For an ultra-silky texture, strain the sauce through a fine-mesh sieve after blending.
Return the sauce to the pan over low heat. Stir in the balsamic vinegar and season with salt and pepper to taste. If using cream, add it now and gently warm through without boiling.