Begin bringing a large pot of water to a boil. Salt it with 2 teaspoons of kosher salt. While waiting for it to boil, start on your vodka sauce. When it's boiling, add the pasta and cook until just before al dente.
Pour the olive oil into a large sauté pan over medium heat. Put the diced yellow onion in the pan and cook until they begin to get some color, about 5 minutes. Add the garlic, oregano, basil, thyme, red pepper flakes and stir them gently in the oil and onions for a minute to get them fragrant.
Add the cherry tomatoes to the pan and sauté for about 10 minutes, until the tomato skins burst. Let them simmer in the pan for another 5 minutes, mush them a little with a wooden spoon to let them get jammy and reduce some of the liquid.
Turn the heat off and pour the tomato sauce into a high powered blender. Blend until smooth, then pour the tomato sauce back into the sauté pan.
Get the pan back onto medium heat. Whisk in the vodka, let the alcohol evaporate for 3 minutes, then stir in the heavy cream. Taste for seasoning and season with kosher salt and black pepper as needed. Turn the heat to low.
Toss the cooked pasta in the sauce, it'll finish cooking in it, absorbing the flavors.
Add the parmesan cheese, stirring until the parmesan is completely incorporated. Add the cubed butter and stir until the butter is just melted in.
Serve hot and top with more basil and parmesan cheese.