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. Whisk in flour until lightly browned, about 1 minute.
Gradually whisk in milk and oregano. Cook, whisking constantly, until incorporated, about 1-2 minutes. Stir in half and half and Parmesan until slightly thickened, about 1-2 minutes. If the mixture is too thick, add more milk as needed; season with salt and pepper, to taste.