Heat the olive oil in a large skillet over medium heat. Add the garlic and shallot and cook until translucent, 2 to 3 minutes. Add the tomato paste and cook until brick red, about 2 minutes. Add the vodka and cook until the liquid has mostly evaporated, about 1 minute more. Add the cherry tomatoes, red pepper flakes, ¼ teaspoon salt and ½ cup water. Raise the heat to medium high and cook, crushing the tomatoes with a wooden spoon a bit as they cook, until the tomatoes break down and become saucy, 6 to 7 minutes.

Carefully transfer the tomato mixture to a blender and blend until smooth, then return to the skillet over medium-low heat. Swirl in the heavy cream, then add the beans, basil sprig and salt and black pepper to taste. Lightly simmer over medium-low heat until the beans are creamy and infused with flavor, 10 to 15 minutes. If the sauce gets too thick, add more water 1 tablespoon at a time. Turn off the heat. Remove the basil sprig and stir in the Parmesan.

Top with plenty of freshly grated Parmesan, a drizzle of extra-virgin olive oil and a few basil leaves. Serve with crusty bread to sop up the sauce.