Bring a large pot of salted water to a boil. Add the chopped potatoes, and cook until tender when pierced with a fork, about 10-15 minutes. Drain potatoes, and mash with a little milk, butter, salt, and pepper to taste. Stir in the fresh thyme. Set aside.
Preheat the oven to 400° F. Place 6 small ramekins on a cookie sheet, and set aside.
In the bowl of a food processor, add flour, egg, milk, and a large pinch of salt. Process to make a smooth batter.
Place 1 teaspoon of butter in the bottom of each of the ramekins. Place the tray of ramekins in the oven for 2-3 minutes, until the butter is melted and very hot.
Working quickly, pour about 1 tablespoon batter into each of the ramekins. Add a heaped tablespoon of mashed potatoes into the center of the batter, and top with another tablespoon of remaining batter in each ramekin.
Place in the oven, and bake until puffy and golden brown, about 15-25 minutes.
Use an offset spatula to carefully remove the Mashed Potato Puffs from the ramekins, and serve warm.