Pat the chicken dry and season both sides with salt and pepper.
In a large skillet over medium heat, add 1 tbsp olive oil. Cook chicken until golden and cooked through, about 4–5 minutes per side. Remove and slice.
In the same skillet, add remaining olive oil and garlic. Sauté until fragrant, about 30 seconds.
Whisk almond milk and cornstarch in a small bowl until smooth. Pour into skillet and stir constantly until thickened, around 4 minutes.
Stir in Parmesan cheese and reduce heat to low.
Add zucchini noodles and sliced chicken to the skillet. Toss gently until coated and warmed through, about 2–3 minutes.
Top with chopped parsley and serve immediately.