How to Make It
Cook pasta in a large pot of generously salted water according to package directions for al dente; before draining, ladle 1 cup pasta water into a large, heatproof bowl. Drain cooked pasta. Whisk cream into reserved pasta water. Set aside.
Melt butter with oil in a Dutch oven or other heavy-bottomed pot over medium. Add shallots and ½ teaspoon salt and cook, stirring occasionally, until golden brown, 8 to 10 minutes. Add garlic; cook, stirring constantly, for 1 minute. Add tomato paste and crushed red pepper; cook, stirring often, until tomato paste starts to darken, 3 to 4 minutes. Add vodka; cook, stirring constantly, until mixture is smooth, about 1 minute.
Reduce heat to low and add reserved cream mixture, several grinds of black pepper, and remaining ½ teaspoon salt. Stir until combined, about 1 minute; add pasta and toss to coat. Serve topped with several more grinds of black pepper.