Peel and smash the garlic cloves; this keeps them intact but releases their flavor.

Slice the shallot into thick ¼-inch slices.

In a nonstick pan, heat olive oil over medium heat and add the smashed garlic and sliced shallot. Let them cook until the bottoms start to brown.

Bring a pot of salted water to a boil and cook the pasta according to package instructions.

Reserve ¼ cup of pasta water before draining.

Remove the garlic and shallots from the pan and discard them.

Stir in the tomato paste and cook for 1-2 minutes until slightly darker.

If using vodka, add it now and let it reduce.

Pour in the heavy cream and whisk until everything combines and starts bubbling gently.

Add the drained pasta to the sauce along with the cold butter and grated parmesan.

Stir well to combine, letting the butter emulsify with the sauce.

If necessary, thin the sauce with reserved pasta water.

Season with salt and pepper to taste, and serve hot, garnished with more parmesan.