Step 1Heat the oven to 325 degrees. Spread pine nuts on a baking sheet and toast in the oven for 8 to 10 minutes, until lightly browned. Let cool.
Step 2Using a mortar and pestle, pulverize the pine nuts, garlic, basil, parsley and salt into a smooth paste. Slowly drizzle in the olive oil and add the Parmigiano-Reggiano, mixing well to incorporate. Just before serving, season with lemon juice and additional salt to taste. Makes three-fourths cup.
Step 1Heat the oven to 200 degrees. Place the tomatoes with vines intact on a wire rack set on a baking sheet. Brush with 1 tablespoon of the olive oil and season with salt and pepper. Roast 4 to 4 1/2 hours, until the skins begin to shrivel like a raisin but the tomatoes remain plump. (Sweet 100s will take considerably less time.) Remove from the oven and allow to cool to room temperature.
Step 2Divide the cheese evenly and place it cut side up onto four small plates. Season the cheese lightly with sea salt (skip this step if using mozzarella di bufala). Spoon 1 tablespoon of pesto sauce over each portion. Using scissors, snip a basil leaf over each portion. Top with tomatoes, divided evenly among each plate, leaving the vine intact (use scissors to cut the vine for each serving).
Step 3Drizzle the tomatoes with olive oil (about one-half teaspoon per serving) and serve immediately.