Cook pasta in 3 quarts boiling water until just tender to bite, about 8 minutes.
Meanwhile, in a 10- to 12-inch frying pan over medium heat, stir garlic in oil until limp, about 2 minutes. Add cheese, broth, and peas and stir until simmering, 4 to 5 minutes.
Drain pasta; return to pan. Add cheese mixture to pasta and mix well. Add mint and mix again. Add to taste salt, pepper, and juice from lemon wedges.