Preheat the oven to 500 degrees F (260 degrees C) and place oven rack in upper-middle position. Grease a high-rimmed metallic baking sheet with butter.
Combine melted butter, thyme, salt, and pepper in a bowl. Add potatoes and toss until fully coated. Place potato slices in a single layer on the prepared baking sheet.
Roast in the preheated oven until slightly golden, about 15 minutes.
Flip potatoes over and roast for another 15 minutes.
Flip potatoes and add vegetable broth and garlic; roast until tender, about 15 minutes.
