Preheat your oven to 500°F (260°C) with a pizza stone inside. Let it heat for at least 30 minutes.
In a food processor, combine roasted red peppers, toasted walnuts, garlic, Parmesan cheese, lemon juice, and olive oil. Blend until smooth. Season with salt, pepper, and red pepper flakes if using.
Roll out the pizza dough on a lightly floured surface until about 12 inches in diameter.
Transfer the dough to a floured pizza peel or parchment paper.
Spread a generous layer of the red pepper & walnut pesto evenly over the dough, leaving a small border for the crust.