Scrub the mussels under cold running water to remove any dirt or sand. Discard any mussels that are cracked or open.
In a large pot, heat the olive oil over medium heat. Add the minced garlic and cook until fragrant, about 1 minute.
Add the white wine to the pot and bring to a simmer. Add the mussels to the pot, cover with a lid, and cook until the mussels have opened, about 5-7 minutes. Discard any mussels that do not open.
While the mussels are cooking, bring a large pot of salted water to a boil. Cook the linguine according to package instructions until al dente.
Once the linguine is cooked, drain it and add it to the pot with the mussels. Toss to combine and season with salt, pepper, and red pepper flakes.
Serve the linguine and mussels in bowls, topped with freshly chopped parsley and grated Parmesan cheese.