Step 1: Prepare the Garlic Scapes. Wash your fresh garlic scapes thoroughly. Trim off the tough, fibrous end and the flower bud, if present, which can sometimes be woody. Chop the tender green stalks into 1-inch pieces. For a brighter green pesto and a slightly milder flavor, you can blanch the chopped scapes in boiling salted water for 30 seconds, then immediately transfer them to an ice bath. Drain well and pat dry before proceeding.
Step 2: Toast the Pine Nuts. In a small, dry skillet over medium-low heat, gently toast the pine nuts for 2-3 minutes, stirring frequently, until they are lightly golden and fragrant. Be careful not to burn them. Immediately remove them from the pan and set aside to cool.
Step 3: Make the Garlic Scape Pesto. In the bowl of a food processor, combine the chopped garlic scapes, toasted pine nuts, freshly grated Parmesan cheese, fresh lemon juice, and a pinch of salt and black pepper. Pulse several times until the mixture is finely chopped. While the food processor is running, slowly drizzle in the extra virgin olive oil until a smooth, bright green pesto forms. You might need to scrape down the sides of the bowl once or twice. Taste and adjust seasoning as needed.
Step 4: Cook the Pasta. Bring a large pot of heavily salted water to a rolling boil. Add your desired pasta and cook according to package directions until al dente. Before draining, reserve about 1 to 1.5 cups of the starchy pasta cooking water.
Step 5: Combine and Serve. Drain the pasta and immediately transfer it back to the warm pot or a large mixing bowl. Add the prepared garlic scape pesto, a splash of the reserved pasta water (start with about half a cup), and the heavy cream. Toss vigorously, allowing the heat from the pasta to gently warm the pesto and cream, creating a luscious sauce that clings beautifully to each strand. If the sauce seems too thick, add more pasta water, a tablespoon at a time, until you reach your desired consistency. Serve immediately, garnished with extra grated Parmesan, toasted pine nuts, and a grind of fresh black pepper.