Remove the dough from the can, unroll it on to a lightly floured surface, and let it stand for 15 minutes or so to come to room temperature
Roll the dough (or pat with your hands) into one big sheet large enough to enclose the cheese round. Spread the surface with the pesto and sun-dried tomato paste, leaving a one-inch border around the sides. Sprinkle with the oregano. Place the cheese in the center of the pastry sheet.
Fold the dough over the cheese so it is fully encased. Place seam side down on a rimmed baking sheet.
In a small bowl, beat the egg with the olive oil. Brush the top of the dough with the egg wash.
Bake until the dough is golden brown, 15 to 20 minutes.
For the Pesto:
In a food processor, pulse the basil, garlic, and pine nuts together until coarsely chopped. Slowly pour in the oil and process until fully incorporated and smooth. Remove to a bowl.
Stir in the cheese and season with salt and pepper. Use that day, or put the pesto in an airtight container and store in the refrigerator for a few days.
Once upon a time, tomato aspics were the brilliant red centerpieces of luncheon buffets. They were peppered with pimento-stuffed olives or crisp bits of celery, chilled in ring-shaped molds, and turned out onto lettuce-lined trays.