Break meat into 1 1/2-inch clumps (do not mix meats). Heat 2 tablespoon oil in a 12-inch heavy skillet over medium-high heat until it shimmers. Cook meat with cumin, 1/2 teaspoon salt, and 1/4 teaspoon pepper over medium-high heat, turning occasionally, until pale golden in spots (insides will not be fully cooked), about 3 minutes. Transfer meat with a slotted spoon to a plate.
Add remaining 2 tablespoons oil to skillet and cook onion, carrots, and garlic over medium-high heat, stirring occasionally, until onion begins to turn golden, 5 to 8 minutes.
Add vermouth and red-pepper flakes and bring to a boil. Whisk cornstarch into broth, then stir into onion mixture and return to a boil, stirring. Reduce heat and simmer, stirring occasionally, until slightly thickened, about 3 minutes.
Stir in meat, juices from plate, celery, and lemon juice and simmer until meat is just cooked through, about 3 minutes.
Cook linguine in a pasta pot of boiling salted water (2 tablespoons salt for 6 quarts water) until al dente. Reserve 1/2 cup pasta-cooking water, then drain pasta. Add to meat along with celery leaves and cook over medium-low heat until just heated through. Add cooking water to moisten if needed. Season with salt and pepper.