Bring 6 quarts of salted water to a boil in an 8-quart pot over high heat.
Pour tomatoes and their liquid into a food processor. Using quick on/off pulses, process until finely chopped (avoid over-processing to prevent turning pink).
Add penne to boiling water and cook semi-covered, stirring occasionally, for 8-10 minutes until al dente.
Meanwhile, heat olive oil in a large skillet over medium heat. Whack garlic cloves with the side of a knife and add to hot oil.
Cook garlic, shaking skillet, until lightly browned, about 3 minutes.
Carefully slide chopped tomatoes into the skillet. Bring to a boil, season with salt and crushed red pepper, and boil for 2 minutes.
Pour in vodka, reduce heat to a lively simmer, and cook until pasta is ready.
Just before pasta is done, remove garlic cloves from sauce and pour in cream. Add butter or oil if using, swirling to incorporate.
Transfer pasta directly to sauce using a wire skimmer, or drain pasta and return to pot with sauce.
Bring sauce and pasta to a boil, stirring to coat. Check seasoning and adjust as needed.
Sprinkle parsley over pasta and boil until sauce clings to pasta.
Remove from heat, add 3/4 cup cheese, and toss. Serve immediately with additional cheese.