Prepare the Garlic and Anchovy Paste: On a cutting board, finely mince the garlic and anchovy fillets. Add the salt and, using the flat side of your knife, mash them into a smooth paste. Transfer the mixture to a small bowl.
Make the Caesar Dressing: Add the mayonnaise, Dijon mustard, lemon juice, black pepper, olive oil, and parmesan cheese to the bowl. Whisk until the dressing is smooth and creamy.
Preheat the Oven: Preheat the oven to 425°F.
Prepare the Asparagus: Wash the asparagus and trim off the woody ends.
Season the Asparagus: Place the asparagus on a sheet pan and toss it with ¼ cup of Caesar dressing, until evenly coated.
Roast the Asparagus: Roast for 8 to 12 minutes, until the asparagus is tender but still has a slight bite.
Serve: Serve immediately while warm.