In a large pot of salted water, cook pasta al dente according to package directions. While your pasta is cooking, prep your asparagus by trimming the ends and chopping the spears up into 1/2-inch long pieces.
Add butter to a large skillet over medium-high heat. When it's pretty much fully melted, add shallots, asparagus, peas, and salt. Sauté until the veggies turn bright green and tender (about 6 to 7 minutes). Add minced garlic and sauté until fragrant (about 1 minute). Remove from heat.
Empty the cooked asparagus mixture into a very large bowl, making sure to scrape up any bits stuck to the pan. To the same bowl, add vegan yogurt and vegan parmesan. Using a slotted spoon, add the hot pasta directly out of the pasta water into the bowl. Mix the ingredients vigorously until well-combined. If the pasta mixture is too dry, add cooked pasta water, 2 tablespoons at a time, and mix until you achieve a creamy texture. Garnish with fresh parsley, cracked black pepper, and chili oil.