Use a spiralizer to turn the zucchini into noodles. Set them aside in a large bowl while you prepare the rest of the meal.
Heat a grill or grill pan over medium-high heat. Season the chicken breasts with salt and pepper, then brush with 1 tablespoon olive oil. Grill for 6 to 7 minutes per side until cooked through. Remove from heat and let rest for 5 minutes before slicing.
Warm the remaining tablespoon of olive oil in a large skillet over medium heat. Add the minced garlic and cook for 30 seconds until fragrant.
Add the asparagus pieces to the skillet. Cook for 3 to 4 minutes, stirring often, until they start to soften.
Stir in the halved cherry tomatoes. Cook for another 2 minutes until the tomatoes begin to release their juices.
Add the zucchini noodles to the skillet. Toss gently for 2 minutes until just warmed but still firm.
Remove the skillet from heat. Stir in the chopped basil and season with salt and pepper to taste.
Divide the zucchini noodle mixture among four plates. Top each serving with sliced grilled chicken and a sprinkle of Parmesan cheese.