Cook the Pasta: Bring a large pot of salted water to a boil and cook the pasta according to package directions (about 10 minutes).
Caramelize the Base: In a large pan or skillet, heat the olive oil over medium heat. Add the chopped onion and cook until translucent. Add the sliced mushrooms and sauté until they are beautifully golden brown.
Sear the Chicken: Add the diced chicken and minced garlic to the pan. Cook until the chicken is no longer pink. Season generously with salt and pepper.
Add the Greens: Add the asparagus pieces and continue to sauté for 3-4 minutes, or until they are tender-crisp.
Simmer the Sauce: Reduce the heat to low. Pour in the cream and add the grated Parmesan. Stir well and let the sauce simmer gently for about 2 minutes, until it starts to thicken.
The Final Mix: Drain the pasta (reserve a small cup of the pasta water). Add the pasta directly into the skillet with the sauce. If the sauce is too thick, add a splash of the reserved pasta water to reach the desired consistency. Serve immediately.