Prepare pasta to package instructions and drain (do not rinse).
Meanwhile, steam the asparagus spears until tender. Cut into 1" pieces.
In a large saute pan over medium-high heat, add the oil and onion slices. Saute for about 3-5 minutes before adding the mushrooms.
Saute the mushrooms for an additional 5 minutes and if using garlic, add now. Saute for 30 seconds and then add the vegetable broth.
Allow to reduce slightly. Add the corn and peas.
When the broth has reduced and the vegetables have cooked through, add the drained pasta (a little residual pasta water will actually help thicken the sauce) and asparagus pieces.
Add the coconut milk, lemon juice and vegan parmesan stirring to combine. If necessary, add a splash more vegetable broth. The pasta will continue to absorb the liquids as it sits.
Season with salt and pepper, to taste.
To serve, divide between four bowls and top with additional vegan parmesan.
Garnish with parsley and/or lemon zest.