Season chicken breasts with salt and pepper. Heat olive oil in a large skillet over medium heat. Add chicken and cook for 5–6 minutes per side, or until golden brown and cooked through (internal temp 165°F). Remove from the skillet and let rest before slicing.
In the same skillet, add butter and minced garlic. Cook for 1 minute until fragrant.
Stir in the chopped sun-dried tomatoes, lemon juice, and zest. Simmer for 2–3 minutes to allow flavors to meld.
Add spiralized zucchini to the skillet and toss gently in the sauce. Cook for 2–3 minutes, just until slightly softened but still firm.
Slice the chicken and add it back to the skillet along with fresh parsley. Toss to combine.
Sprinkle with parmesan cheese before serving warm.