Heat a pan over medium heat. Add one tablespoon olive oil once it's hot, swirl, then add the tomatoes and salt. Cook uncovered for 8 to 9 minutes, stirring occasionally, as tomatoes burst open and their juices cook. The finished result will be concentrated and jammy, not runny.
Once tomatoes are at that stage, add 2 more tablespoons olive oil and garlic. Cook for 1 to 2 minutes, stirring, until garlic becomes fragrant. Remove from heat and stir in basil. Then put the tomato mixture onto a plate and into the fridge for at least 10 minutes to cool.
Add mozzarella, ricotta, salt, and lemon juice to the bowl of food processor. Process for 30 seconds, then stop and scrape down sides. Turn food processor back on and add cream while it is running. Process for 30 seconds, then stop and scrape down sides. Turn back on and process for one minute.
Spread whipped mozzarella onto a plate or a shallow bowl. Then put tomato mixture on top and gently spread, so that it leaves just about a one inch border of the cheese showing. This is so each bite gets the cheese and topping.
Grate one lemon evenly over the top of the dip (do not skip this step - it makes such a difference in the combination of flavors), and finish with fresh basil. Serve cold or at room temp with crackers or bread.
