Melt 1 tablespoon butter in a saucepan over medium heat. Add
zucchini and cook, stirring occasionally, until tender and heated through,
about 3-5 minutes; set aside.
Melt remaining 2 tablespoons butter in the saucepan. Add
garlic, and cook, stirring frequently, until fragrant, about 1-2 minutes. Gradually
whisk in cream, broth, thyme and oregano. Cook, whisking constantly, until starting
to thicken somewhat. Stir in Parmesan and cook until desired thickness, about
1-2 minutes. If the mixture is too thick, add more broth as needed; season with
salt and pepper, to taste.
Stir in chicken slices and zucchini and gently toss to combine.
Serve immediately, garnished with parsley, if desired.