Preheat the oven to 375 degrees F.
To make the pesto: In a blender, combine the arugula, spinach, Parmesan, garlic, and sliced almonds. Blend on low and slowly drizzle in the olive oil and the lemon juice. Blend for about 45 seconds, or until the mixture completely emulsifies. Remove from the blender and season with salt and pepper.
To make the galettes: Cut the puff pastry sheets into 6 (6-inch) round circles. Place each circle on a parchment-lined pan. Spread about 3 tablespoons of arugula pesto over the top of each puff pastry circle. Sprinkle the roasted peppers evenly on top. Divide the feta cheese evenly over the top. Bake in the oven for approximately 30 to 35 minutes until the puff pastry is golden brown and the cheese is melted.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.