Mince the garlic, chop the shallot, and trim the stems from the haricots verts. Trim the woody ends from the asparagus and cut into thirds. Optionally, slice some snap peas open.
Heat olive oil in a large, lidded pan over medium-low heat. Add the garlic and shallot and sauté for 2-3 minutes until fragrant, stirring frequently to prevent burning.
Add the haricots verts, asparagus, and snap peas to the pan. Stir for 1-2 minutes, then season with salt and pepper and stir well.
Deglaze the pan with white wine, if desired. Stir and cook for 1-2 minutes.
Add the pasta to the pan, breaking it only if necessary to fit.
Add 3-4 cups of water, or enough to just cover the pasta. Use boiling water to speed up the process if preferred.
Stir the pasta to submerge it, then increase heat to high. Cover and cook for 5 minutes. Uncover and stir; if the pasta is still firm and water is low, add water in 1/4 cup increments and continue cooking covered until al dente.
Consult the pasta packaging for cooking times, ensuring a small amount of liquid remains when the pasta reaches al dente to help form a creamy sauce.
Remove the pan from heat and stir in the juice of half a lemon. Mix in the parmesan cheese until a creamy sauce forms, then fold in the arugula.
Serve the pasta in bowls garnished with extra arugula and freshly shaved parmesan.
