Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius).
Arrange trimmed asparagus on a large rimmed sheet pan and toss with 1 tablespoon of olive oil, 0.25 teaspoon salt, and 0.125 teaspoon black pepper.
Roast asparagus for 5 minutes to initiate fiber softening.
In a small mixing bowl, whisk together the melted butter, remaining 2 tablespoons olive oil, minced garlic, lemon zest, lemon juice, red pepper flakes, and remaining salt and pepper.
Pat shrimp dry with paper towels to ensure proper sauce adhesion and place in a bowl.
Toss shrimp with the prepared butter mixture until evenly coated.
Remove the sheet pan from the oven and distribute the shrimp in a single layer among the asparagus.
Return the pan to the oven and roast for 6 to 8 minutes, or until the shrimp reach an internal temperature of 120 degrees Fahrenheit and appear pink and opaque.
Remove from oven and garnish immediately with minced parsley and grated Parmesan cheese.