This cooking method produces the tastiest lobsters. The more traditional one immerses them in a large pot of boiling water.
Pour 1 inch of water into large stockpot; bring to a boil. Add lobsters, head first, cover, and cook until meat is opaque, 12 to 15 minutes. Remove from pot; transfer to cutting board back-side down.
Meanwhile, whisk mustard, vinegars, and salt and pepper to taste. Slowly whisk in oil until combined; set aside.
Toss together the tomatoes, basil, and 3 tablespoons vinaigrette, and set aside.
Using a sharp large knife, cut the lobsters in half down the middle. Divide the pea shoots among four dinner plates, and place the lobsters on top. Fill the body cavities with the tomatoes, and sprinkle with pepper. Serve the remaining vinaigrette on the side.