Heat a large sauté pan over medium-high heat, add the mussels and a small ladleful of water and cover the pan. Sauté until the shells open, about 2 to 4 minutes, shaking the pan occasionally. Remove the pan from the heat.

Using a fine-mesh sieve, strain the mussels over a bowl to get rid of any sand and grit, reserving the juices. Discard the unopened shells. Remove the meat from the remaining shells and place in the bowl with the juices.

Bring a large pot of water to a rolling boil. Salt the water and drop in the pasta. Cook until the pasta is just under al dente, tender but firm to the bite, stirring occasionally with a wooden spoon. Drain the pasta in a colander, reserving about 1 1/2 cups of the pasta cooking water.

Meanwhile, in a large sauté pan over medium heat, combine the olive oil, garlic, pepper flakes, and parsley and briefly sauté until the garlic just begins to soften. Stir in the reserved mussels and their juices and let reduce for about 2 minutes or so, depending upon the amount of liquids in the pan.

Add the pasta to the pan and toss well to coat with the sauce, about 2 minutes. Remove the pan from the heat and add the pecorino and mint. Toss and stir until the cheese has melted and the pasta is nicely coated with the sauce, adding a small ladleful of the pasta cooking water, if more liquids are needed in the pan.

Divide the pasta among the plates and serve immediately.