Place Mozzarella or Brie in the freezer for 20 minutes to firm up. This will make it easier to cut.
In a large serving bowl, add your rough cut tomatoes and smashed garlic.
Roll up basil leaves together like a cigar and run your knife through them creating thin ribbons of basil. Rip your basil, and it will blacken. And no one wants blackened basil! Add to tomatoes and garlic.
Pour olive oil over tomato, basil, and garlic mixture, seasoning generously with Kosher salt and freshly ground pepper to taste. Gently fold the mixture together.
Remove cheese from freezer and using a large chef's knife, cut Mozzarella/Brie into cubes (If using Brie, remove rind first and cut/tear into irregular pieces).
Add cheese to olive oil mixture and stir gently to incorporate.
Cover your serving bowl (see Jule's summertime favorites below) with a clean dish towel and allow to sit at room temperature for 2-8 hours. The longer the better.
When you are ready to eat, cook pasta according to directions (here's my favorite high fiber pasta), drain and, while piping hot, pour pasta into your serving bowl, mixing as you go. Stir until well-combined.
Serve immediately and sprinkle freshly grated Parmigiano-Reggiano generously.