Salt the tomatoes: Chop the cherry tomatoes and toss them with the salt. Place them in a strainer over a bowl and let them sit for 10 minutes to release excess liquid.
Preheat the oven: Set the oven to 375°F while you prepare the cheese base, so it's fully heated by the time the dip is assembled.
Mix the cheese base: In a bowl, stir together the softened cream cheese, 1 cup of the mozzarella, minced garlic and black pepper until smooth and evenly combined.
Spread into the dish: Press the cheese mixture into an even layer in a small oven-safe baking dish or cast iron skillet.
Dry the tomatoes: Pat the drained tomatoes with a paper towel to remove any remaining moisture before adding them to the dish.
Layer the toppings: Scatter the dried tomatoes over the cheese base, then top with the remaining 1 cup of mozzarella and the parmesan cheese.
Bake until golden: Bake at 375°F for 18-20 minutes, until the cheese is melted and blistered into golden-brown spots at the edges.
Prepare the bread: While the dip bakes, slice the Italian bread, brush with olive oil, and toast lightly until the edges turn golden.
Add basil and balsamic: Remove the dip from the oven and scatter the sliced fresh basil over the top, then drizzle with balsamic glaze.
Serve warm: Set the dip out alongside the toasted bread and crackers for dipping while it's still warm and the cheese is soft.