Adjust the oven rack to the middle position and heat the oven to 375°F. Melt the butter in a 12-inch nonstick skillet over medium heat.

Add the onion and cook, stirring often, until golden brown, about 10 minutes. Watch closely toward the end to ensure the edges don't scorch.

Stir in the potatoes, thyme, salt, and pepper. Increase the heat to medium-high and cook, stirring occasionally, until the potatoes are tender and lightly browned, 6 to 8 minutes. Stir in the sun-dried tomatoes and remove the skillet from the heat.

Spread the potato mixture evenly into the pre-baked tart shell. Cut the Camembert wheel in half through the middle to create two thin discs, then cut each half into four wedges. Arrange the cheese wedges over the top of the tart with the rind side facing up.

Place the tart on a baking sheet and bake until the pastry is golden and the cheese is melted and bubbling, 25 to 35 minutes, rotating the sheet halfway through for even browning.

Let the tart cool on the sheet for 10 minutes to allow the filling to set. Remove the outer metal ring of the tart pan, slide a thin spatula between the tart and the bottom plate, and carefully transfer to a platter. Serve warm while the cheese is still soft and gooey.