To prepare the filling, place diced tomatoes in a bowl. Add pesto and L&B Parmigiano-Reggiano. Toss to coat the tomatoes. Set aside.
Heat the grill to high.
Trim the stem ends off the zucchini and slice each one lengthwise. Using a teaspoon, scrape the seeded pulp out of each zucchini half to form a hollow shell. Brush both sides of each zucchini half with olive oil and sprinkle with sea salt.
Turn the grill down to medium-high and place the zucchini halves on the grill cut-side down; grill for 6 to 8 minutes, or until each one is tender yet slightly firm. Remove the zucchini halves from the grill and place them in a baking dish, hollow side up.
Divide the tomato filling between the zucchini halves. Return the zucchini to the grill cut-side up to warm for 10 minutes. Serve immediately.
Optional: Sprinkle with more grated Parmigiano-Reggiano right before serving