Preheat an oven to 220 degrees C. Place the beetroot, 1 clove of chopped garlic and the olive oil on a piece of aluminum foil; fold the foil around the beetroots into a sealed packet.
Roast in the preheated oven until easily pierced with a fork, 40 minutes to 1 hour. Let beetroot cool just until they can be handled, then rub with a paper towel to remove skins. Chop into cubes; set aside.
Heat the peanut oil and butter in a wok or frypan over medium-high heat. Cook and stir bok choy and the remaining garlic together until bok choy is slightly softened but still crunchy, a couple of minutes. Remove from heat; stir in the beetroot and the feta. Serve warm.