Preheat the oven to 425 degrees.
Core the tomatoes and then slice them across (not through the stem) in 1/2 inch-thick slices. Arrange the slices in a single layer on a sheet pan. Drizzle the tomatoes with the olive oil and sprinkle with the oregano, 1 1/2 teaspoons salt, and the pepper.
Bake the tomatoes for 10 minutes. Remove them from the oven, spread each slice with Pesto, and sprinkle with the Parmesan cheese. Return the tomatoes to the oven and continue baking for 7 to 10 minutes, until the Parmesan is melted and begins to brown. Using a flat metal spatula, put the tomatoes on a serving platter, sprinkle with extra salt, and serve hot, warm, or at room temperature.
Place the walnuts, pine nuts, and garlic in the bowl of a food processor fitted with the steel blade. Process for 30 seconds. Add the basil, salt, and pepper. With the processor running, slowly pour the olive oil into the bowl through the feed tube and process until the pesto is pureed. Add the Parmesan and puree for a minute. Use immediately or store the pesto in the refrigerator or freezer with a thin film of olive oil on top.
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