Slice off a thin piece from the bottoms of the tomatoes and set them, cut side down, on a parchment paper lined baking sheet. Cut out the stem end of each tomato, making a "crater" about 1/2" deep. Drizzle with 1 tsp olive oil and sprinkle with salt and pepper. Roast at 350°F for 10 minutes.
Meanwhile, slice prosciutto in half lengthwise. Place them so as to make an "X" and place a piece of bocconcini cheese in the centre of each X. Wrap prosciutto around cheese to cover.
Place a heaping tsp of pesto in each tomato crater. Top with wrapped cheese. Drizzle with more olive oil and bake again for another 5-7 minutes or until cheese softens. Garnish with more pesto and serve immediately.