Cook pasta according to package directions. Reserve 1 cup pasta water, then drain.
Heat 2 tbsp. oil in a large frying pan over high heat. Add mushrooms and cook until browned, about 5 minutes. Stir in leek and garlic and cook until fragrant, about 1 minute. Add greens, radicchio, and salt and cook until just warm, about 1 minute (add a bit of water if pan starts to scorch).
Toss pasta, vegetables, and reserved pasta water together. Top with dollops of ricotta, croutons, a drizzle of remaining 2 tbsp. oil, and parsley.