Optional: gently toast the walnut halves in a saucepan just until golden.
Remove and set aside.
Break off the tough root ends of the asparagus and set aside for future use in a soup.
Cut off the asparagus tips, about 5-6 cm long pieces.
Cut the rest of the asparagus in half. You should have pieces that are about 5 to 6 cm (2 to 2 ⅓ inches) long.
Cut the asparagus pieces in half lengthwise (or in quarters depending on the thickness of the asparagus).
Cook the asparagus in a saucepan with a small amount of lightly salted boiling water + 2 tablespoons extra-virgin olive oil just until the asparagus are tender-crisp.
Use only enough water to cover the asparagus about halfway.
It should take no more than 3 to 5 minutes to cook.
Drain the asparagus and set aside, but reserve the asparagus cooking water.
Add the butter, lemon juice & lemon zest, the asparagus, and the freshly grated Parmesan cheese to the saucepan and cook on high for just 30 seconds.
You should have a thick, creamy sauce.
If necessary add some of the asparagus cooking water by the tablespoonful to the sauce but only if it's too dry.
Remove the asparagus tips from the sauce to set atop the ravioli when you serve.