Preheat the oven to 425°F (220°C).
Toss the grape tomatoes with the olive oil and a sprinkle of salt. Spread them into a single layer on a parchment- or foil-lined baking sheet and roast for about 20 minutes, until blistered and jammy.
1½ cups (225 g) grape tomatoes, 2 tbsps (30 ml) olive oil, ¼ tsp (1 g) kosher salt
Meanwhile, bring a large pot of generously salted water to a boil. Heat a large skillet over medium heat with the olive oil. Add the shallot and cook until softened, about 3 to 4 minutes. Stir in the garlic, tomato paste, red chili flakes, and smoked paprika. Cook for 2 to 3 minutes, stirring often, until the tomato paste darkens slightly.
1 tbsp (15 ml) olive oil, ¼ cup (40 g) finely chopped shallots, 3 cloves garlic, ¼ cup (66 g) tomato paste, 2 -3 tsps (4 - 6 g) red pepper flakes, ½ tsp (1 g) smoked paprika
Pour in the vodka and cook for 1 to 2 minutes to let the alcohol cook off. Add the roasted grape tomatoes, gently crushing some with the back of a spoon while leaving others mostly intact. Stir in the heavy cream, honey, lemon juice, salt, and black pepper. Simmer for 3 to 5 minutes, until the sauce thickens slightly.
¼ cup (60 ml) vodka, ½ cup (120 ml) heavy cream, 1 tsp (7 g) honey, 1 tbsp (15 ml) fresh lemon juice, 1 tsp (6 g) kosher salt, ½ tsp (1 g) coarsely ground black pepper
Cook the pasta until al dente according to the package directions. Before draining, reserve 1 cup (240 ml) of the pasta cooking water.
16 oz (454 g) mezzi rigatoni
Add the drained pasta to the skillet with a splash of the reserved pasta water. Stir in the butter and ½ cup (50 g) of the Parmesan, tossing continuously until the butter melts and the cheese is fully incorporated. Add more pasta water as needed until the sauce becomes silky and coats the pasta.
2 tbsps (28 g) unsalted butter, ¾ cup (75 g) finely grated Parmesan cheese
Divide among serving bowls and finish with the remaining ¼ cup (25 g) Parmesan and the chopped basil. Garnish with additional fresh basil, if desired, and serve immediately.
2 tbsps (6 g) chopped fresh basil