Bring a large pot of heavily salted water to a boil.

In a large sauté pan over medium heat, add olive oil and the minced shallot. Cook until soft and translucent, about 2–3 minutes.

Stir in the garlic and cook for 30 seconds until fragrant.

Add the tomato paste and cook, stirring constantly, for 3–4 minutes until it deepens to a brick red color and begins to caramelize.

Deglaze with vodka and let it simmer for 2–3 minutes until mostly reduced and the alcohol cooks off.

Stir in the heavy cream. Season with salt, pepper, and red pepper flakes if using. Simmer gently until the sauce becomes smooth and blush pink.

Cook the mezzi rigatoni until just shy of al dente. Reserve 1 cup pasta water before draining.

Add the pasta directly to the sauce along with a splash of pasta water and toss to combine.

Add the cold butter and grated Parmigiano. Toss vigorously until the sauce emulsifies and becomes glossy and silky, adding more pasta water as needed.

Finish with extra Parmigiano and serve immediately.