Heat the oven to 356°F (180 °C). Prepare a ceramic tray about 11″ (28 cm) x 8″ (20 cm).
Peel the potatoes and cut them down the middle into large cubes. Cut off the uneven parts along the sides. You can use a potato peeler very carefully to even off their bottom part to allow them to sit upright.
Heat the butter with the oil in a pan and place the potato cubes to roast on both sides well until golden. Don't roast their sides.
Take them out and arrange them next to each other, without overlapping, in the tray. Sprinkle with the chopped thyme and pour hot broth and pressed garlic over them. On top of each potato cube place a small piece of butter.
Bake at 356°F (180 °C) until ready.
Notes: In French, Fondant means melt-in-your-mouth, hence the name of these unique potatoes. It originates from the French Fondre - something that melts at high temperature.