Fill a large pot with water, place over high heat and bring to a boil. Add a small handful salt to water and add pasta.
Cook pasta, stirring occasionally, until al dente, 6 to 8 minutes.
Drain pasta, reserving 1/2 cup pasta water, and set both aside.
Place a large skillet over medium heat. Once skillet is hot add oil and sauté shallots and garlic for 3 to 4 minutes, or until aromatics begin to slightly caramelize.
Add tomato paste and stir together. Continue to stir until paste turns bright red,2 to 3 minutes.
Deglaze skillet with vodka and stir together until vodka evaporates. Add reserved pasta water to skillet and stir together until smooth, about 1 minute. Season with salt and pepper.
Stir cream into sauce until mixture is smooth. Reduce heat to medium-low and simmer together, about 3 to 4 minutes. Stir in butter and Parmesan and continue to simmer until sauce is smooth, glossy and has thickened enough to coat the back of a spoon, about 3 minutes.
Add cooked pasta to sauce and toss together until fully coated. Season with salt and pepper.
Serve with more grated Parmesan and black pepper.