Bring a large pot of heavily-salted water to a boil

To cook mushrooms:

Preheat oven to 500 degrees. Toss mushrooms with 2 tablespoons of the olive oil and generous pinches of coarse salt and pepper.

Spread the mushrooms in a single layer on a rimmed baking sheet. Roast in the oven, turning once, for about 10 minutes, until nicely browned. Allow to cool slightly and cut into quarters.

To prepare chive oil:

In a food processor, combine 1/2 cup olive oil with chives and generous pinches of coarse salt and pepper. Process until pureed.

To prepare the pasta:

Cook the pasta until just al dente. Be careful as angel hair may just need about 2 minutes.

Drain, reserving 2 tablespoons of cooking water if serving hot. Toss the pasta with the chive oil and the mushrooms (plus the water if serving hot). Otherwise, let the pasta cool to room temperature.

Serve with lots of grated cheese on the side.