Slice the chicken breasts into even, bite-sized pieces. Pat dry and season lightly with salt and pepper.
Heat a large skillet over medium heat. Add olive oil and half of the butter. When the butter melts and the pan shines, add the chicken pieces. Cook until golden and cooked through, about 5–7 minutes. Remove the chicken and set aside.
In the same skillet, add the remaining butter and the minced garlic. Sauté for about 30 seconds until fragrant; be careful not to burn it.
Pour in the heavy cream and chicken broth. Bring to a gentle simmer, stirring to loosen any browned bits from the skillet.
Stir in the grated parmesan until the sauce thickens slightly. If the sauce looks too thick, add a splash more broth or cream until it reaches your desired consistency.
Return the chicken to the skillet and simmer for 2–3 minutes to meld the flavors. Taste and adjust salt and pepper as needed.
Meanwhile, turn the zucchini into noodles using a spiralizer or a vegetable peeler to create long, ribbon-like strands. Pat the zucchini dry with a paper towel to remove excess moisture.
Add the zucchini noodles to the sauce and toss gently to coat. Cook for 1–2 minutes just until the noodles start to soften but still retain some bite.
Garnish with chopped parsley and, if you like a touch of heat, a pinch of red pepper flakes. Serve immediately.