Cut off the crust from the bread and cut into 1-inch cubes. You should have about 3 cups. Heat 1 tablespoon olive oil in a large saute pan over medium high heat. Add the bread and cook, stirring frequently, until golden and crisp, about 5 minutes. Remove from the heat and dump the bread cubes onto a baking sheet to cool. (Alternately, you can toast these in a 325 F oven for 10 minutes or so.)
Place the sliced shallots in a small bowl and cover with 1 tablespoon red wine vinegar. Let sit while you prep the rest of the ingredients.
Core the large tomatoes and cut into roughly 1-inch chunks. Cut the cherry tomatoes in half, and place all of the tomatoes in a large bowl.
In a small bowl, whisk together the remaining tablespoonful of red wine vinegar with 3 tablespoonfuls of olive oil. Season with salt and pepper.
Scatter the shallots and basil over the tomatoes and drizzle with the vinaigrette. Using your hands, toss gently. Add the bread cubes and gently toss with your hands. Season with salt and pepper to taste.
Place half of the tomato mixture on a platter, scatter with half of the mozzarella, add the remaining tomato mixture and the remaining mozzarella. Drizzle with olive oil and garnish with additional torn basil. Serve immediately as the bread will get soggy.
