Coarsely grind 2 Tbsp. cumin seeds in mortar and pestle or spice mill. Set aside.

Heat ½ cup extra-virgin olive oil in a large high-sided skillet over medium-high. Add 3 large shallots, thinly sliced, and season with kosher salt. Cook, stirring occasionally, until shallots are softened and beginning to brown around the edges, 6–9 minutes.

Add 2 Tbsp. double-concentrated tomato paste and stir to coat shallots. Cook, stirring often, until paste is darkened in color, about 3 minutes.

Add 1 Tbsp. smoked paprika, 1 tsp. crushed red pepper flakes, and reserved cumin seeds. Cook, stirring, until spices are fragrant, about 30 seconds.

Add 1 lb. ground lamb and break up into small pieces with a wooden spoon; season with salt. Cook, stirring occasionally, until lamb is cooked through, about 5 minutes. Reduce heat to low and keep warm.

Cook 1 lb. pappardelle or other wide noodle in a large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving 2 cups pasta cooking liquid. Return pasta to pot off heat.

Increase heat under lamb to medium and add 1 cup pasta cooking liquid; stir to combine.

Add half of lamb and ½ cup coarsely chopped mint to pasta; cook over medium-low heat, tossing and adding more pasta cooking liquid if needed to loosen, until sauce coats pasta, about 2 minutes. Taste and season with more salt if needed.

Divide pasta among bowls; top with remaining lamb in skillet, then with more mint.