Step 1: Preheat the oven to 400 degrees Fahrenheit

Step 2: Wash and chop the asparagus into one-inch pieces

Step 3: Toss the asparagus with 1 tablespoon of olive oil, salt, and pepper to taste

Step 4: Spread the asparagus evenly on a baking sheet

Step 5: Dot the asparagus with the butter

Step 6: Roast the asparagus for 15 minutes until tender and slightly caramelized

Step 7: Remove from the oven and allow the asparagus to cool

Step 8: Meanwhile, bring a large pot of salted water to a boil

Step 9: Cook the pasta according to package instructions until al dente

Step 10: Drain the pasta and cool it completely by running it under cold water

Step 11: In a large mixing bowl, combine the cooled pasta and roasted asparagus

Step 12: Add the chopped sun-dried tomatoes, oil from the sun-dried tomatoes, sliced green onions, Parmesan cheese, parsley, lemon zest, and lemon juice

Step 13: Use a rubber spatula to scrape the butter and oil mixture from the baking sheet into the bowl

Step 14: Toss everything gently but thoroughly until well combined

Step 15: Season the salad with additional salt and pepper to taste

Step 16: Pile the pasta salad into a large serving bowl

Step 17: Garnish with black sesame seeds, extra parsley, and additional Parmesan cheese if desired

Step 18: Serve immediately or refrigerate until ready to serve