Preheat oven to 425º F and line a baking sheet with parchment paper. Bring a large pot of water to boil.

Trim the tough ends from the asparagus and cut the spears crosswise into 1 to 2-inch pieces, keeping the tips separate. Mix 1/2 teaspoon salt and 1 tablespoon olive oil on the prepared baking sheet. Toss asparagus tips in the oil and move them to one side of the baking sheet. Toss the rest of the stems and garlic in the oil and spread them out, keeping them separate from the tips. Roast in the preheated oven until just tender, 8 to10 minutes.

Pulse pine nuts and Parmesan cheese in a food processor until finely chopped. Add the roasted asparagus stems to the food processor (reserving the tips for garnishing) and pulse until the asparagus is coarsely chopped. With the food processor running, pour in the olive oil and process to mix well.

When the water comes to a boil, cook pasta according to the directions on the package. Reserve about 1/2 cup of the pasta cooking water before draining the pasta in a colander.

Return the pasta to the pan and add the asparagus pesto. Mix well and season with salt and pepper to taste. If the sauce needs thinning, add some of the reserved pasta water until it reaches the desired consistency.

Garnish bowls of pasta with reserved asparagus tips, grated Parmesan cheese, and freshly cracked pepper.