Step 1

Stir 2 garlic cloves, finely grated, 1 cup plain whole-milk yogurt, 3 Tbsp. finely chopped mint, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and 1 Tbsp. water in a medium bowl to combine. Chill yogurt sauce while you make the meat sauce.

Step 2

Heat 1 Tbsp. extra-virgin olive oil in a large Dutch oven or other heavy pot over medium. Break 1 lb. ground beef into large (about 3") clumps and add to pot; season with 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt. Cook, undisturbed, until meat is browned underneath and some fat has cooked out, 6–8 minutes.

Step 3

Break up meat with a wooden spoon, then add 2 large onions, finely chopped, and remaining 6 garlic cloves, finely chopped. Stir in 1½ tsp. ground coriander, 1½ tsp. ground cumin, ¾ tsp. cayenne pepper, and remaining 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt. Cook, stirring occasionally, until onions are softened, 6–8 minutes. Add 3 Tbsp. double-concentrated tomato paste and cook, stirring, until tomato paste is darkened in color, about 2 minutes.

Step 4

Pour in one 28-oz. can crushed tomatoes and 2 cups water and stir to combine. Bring to a simmer, then reduce heat to medium-low and cook, stirring occasionally, until sauce is thickened and flavors have come together, 30–35 minutes.

Step 5

About 10 minutes before sauce is done, cook 16 oz. pappardelle, rigatoni, or penne in a large pot of boiling salted water, stirring occasionally, until very al dente, about 2 minutes less than package directions. Using tongs, transfer pasta to pot with sauce. Add 1 cup pasta cooking liquid and cook over medium heat, tossing constantly, until pasta is al dente and sauce is slightly thickened, about 2 minutes.

Step 6

Divide pasta among bowls. Drizzle yogurt sauce over and top with mint leaves.