Bring a large pot of water to a boil.

Place a skillet over medium-high heat and toss in the strips of onions. Once they start to stick, swirl in the olive oil and toss around in the pan until lightly golden.

If you have a microplane, grate the lemon. If you do not, peel the bright yellow skin off of the lemon, leaving as much of the white pith as possible. Place the lemon peel in the milk and warm in a saucepan or microwave. Allow the milk to rest and absorb the oils in the lemon peel. Once the milk is warm, it is time to prepare the béchamel sauce.

Melt the butter in a saucepan. Whisk the butter, while sprinkling in the flour. Stir until the roux becomes lightly golden and has a faint toasty smell. Pour in the warm milk while whisking. Add the grated lemon zest and half of the salt.

Once the sauce is prepared, allow it to simmer on low heat, stirring occasionally. Now, add the pasta and remaining salt to the boiling water to cook.

While the pasta cooks, toss the asparagus pieces in with the caramelizing onions. Drizzle on the lemon juice and toss until the juice is absorbed in the vegetables.

When the pasta is cooked, drain it and toss it lightly with the asparagus and onions. Stir the parmesan cheese in with the milk sauce and add more salt, if necessary, to taste.

Drizzle the béchamel sauce across the pasta and vegetables. Toss and serve with an extra sprinkle of parmesan to garnish.