Bring salted water to boil in a large pot.

While that is happening, slice the garlic and cut the asparagus.

Cut the asparagus in 2-inch length, you will have the tips, and some of the stalks, just not the chewy ends. You can save the chewy ends to make soup later.

Put the pasta in the boiling water.

In a large sauté pan, melt the butter, and sauté the garlic until it has turned translucent.

Add the asparagus, and sauté, then reduce the heat, and cover until the asparagus is crisp-tender, about 5 minutes.

Add the mussels, stir, and cover until they have warmed up about 3 minutes.

Check the pasta, it should be done by now. Don't drain it, just turn the heat off.

Add the wine to the pot, the corn starch, and more butter. Whisk this around, tipping the pan, until the sauce is slightly thickened, about 2 minutes.

Drain the pasta, but put it back in its pan and mix it with the small amount of butter. Then, add that pasta to the mussel mixture. Add the Parmesan cheese, and toss to combine. Garnish with freshly ground black pepper and parsley.