Place a large pot with water over high heat and bring up to a boil. Once boiling, add some salt and the pasta, and cook to al dente according to package directions. Drain thoroughly.
While the water is coming up to a boil, start the shrimp and veggies: Season the shrimp with a little salt and some pepper. Place a large skillet over medium-high heat with 2 tablespoons of olive oil. Once oil ripples, add the shrimp in an even layer. Cook about 2 minutes on each side then remove from the skillet and reserve on a plate.
Return the skillet to the heat with 2 more tablespoons of olive oil. Add mushrooms and cook, without stirring, for 3-4 minutes. Then give the pan a shake and a stir, add the onions and garlic, and continue to cook for another 2-3 minutes or until the mushrooms are brown, the onions are soft and garlic is golden in color.
Add asparagus, some salt and pepper, the sun-dried tomatoes and reserved shrimp, and continue to cook for 2 minutes. Add pasta, toss to coat, taste and season with more salt and pepper. Add parsley and basil, top with Parmigiano Reggiano, stir to combine and serve.