Preheat the oven to 425 degrees . Melt the butter; skim and discard the foam. Brush the bottom and sides of a glass pie plate with some of the melted butter.
Peel and thinly slice the potatoes. Spread the slices on a paper towel and pat dry. In a large bowl, toss the slices with half of the remaining melted butter.
In the buttered pie plate, arrange one-third of the potato slices in an overlapping circular pattern to form a single layer. Season with salt and pepper and one-third of the thyme leaves. Repeat with the remaining potatoes and thyme, pressing down on the layers to ensure an even thickness. Brush the top of the tart with the remaining melted butter and season to taste with salt and pepper.
Bake the potato tart until the bottom is golden brown and the potatoes are cooked through, about 45 minutes.
Slide the tart onto a plate, cut into wedges and serve.