Preheat the oven according to the directions on the flatbread refrigerator pizza dough package.
Combine the herbs, walnuts, Parmesan cheese and roasted garlic in a food processor. Pulse while drizzling in the olive oil.
Season with salt and pepper to taste.
Line a baking sheet with parchment paper. Roll out the flatbread refrigerator pizza dough on the baking sheet.
Spread the tarragon walnut pesto mixture over the dough. Top with the grated cheddar cheese and bake according to the directions on the package until the dough is crisp and the pesto and cheese are hot and bubbly.
Remove from the oven and let cool 5 minutes before cutting and serving.