Mince garlic.

Bring a large saucepan of water to a boil. Cook pasta (possibly in batches) for 6 minutes. Add asparagus and continue cooking, stirring occasionally, until the pasta and asparagus are just tender, about 3 minutes more. Drain and return to the pot.

Meanwhile, whisk milk, mustard, flour, salt and pepper in a medium bowl. Heat oil in a small saucepan over medium-high heat. Add garlic and cook, stirring constantly, until fragrant and lightly browned (should not take more than 3 minutes). Whisk in the milk mixture. Bring to a simmer, stirring constantly, and cook until thickened, 4 to 5 minutes. Stir in tarragon, lemon zest and juice.

Stir the sauce into most, not all, of the cooked pasta (make sure to leave aside a couple of servings for people who don't like lactose or cream) and place over medium-high heat. Cook, stirring constantly, until the sauce is thick, creamy and coats the pasta. Stir 1/4 cup for every 2 servings Parmesan into the pasta until combined. Serve the pasta topped with the remaining 1/4 cup for every 2 servings Parmesan.