Preheat the oven to 400 degrees F. Brush a baking dish with oil or line a deep, rimmed baking sheet with aluminum foil, making sure the foil overlaps the edges. 

Wash the potatoes and pat dry.

Use a sharp knife to make thin cuts in each potato from the short sides leaving about a 1/4 inch uncut at the base of each potato.

Arrange the potatoes in the baking dish or on the baking sheet. Brush the cut potatoes with the olive oil and season with kosher salt and freshly ground pepper.

Place the dish in the oven and bake for 20 minutes.

In a separate bowl, mix together the heavy cream and vegetable broth.,

Remove the potatoes from the oven and evenly pour the cream mixture over the tops of the potatoes. Use a brush to make sure the sauce gets into the crevices of the cut potatoes.

Distribute the shredded cheese over the top then sprinkle the fresh thyme over the cheese.

Return the potatoes to the oven and bake for another 30 minutes.

Remove from oven, season again with kosher salt and freshly ground pepper to taste. Garnish with thyme sprigs and serve.