Prepare the pasta according to package instructions.
In a mixing bowl, toss the cooked pasta with a tablespoon of the olive oil and season with salt and pepper. Set the pasta aside.
Meanwhile, in the cup of a blender, combine the basil, pine nuts, garlic, and cheese. Blend thoroughly and season with salt and pepper.
While the blender is still running, drizzle in one cup of the oil. The mixture will be thick. Season with salt and pepper and set aside.
Preheat the grill.
Toss the scallops with a tablespoon of the olive oil, salt and pepper.
Place the scallops on the grill and cook for two to three minutes on each side or until they're firm to the touch.
In a sauté pan, over medium heat, add the remaining oil. When the pan is hot, add the tomatoes, season with salt and pepper, and sauté for about two minutes.
Add the asparagus and mushrooms. Continue to sauté for three to four minutes or until the mushrooms begin to wilt.
Toss the pasta with the vegetables and the pesto. Mix well.
Add the cheese and combine thoroughly. Readjust seasonings if needed.
Mound the pasta in the center of serving plate. Place the scallops on top of the pasta. Garnish with parsley.