Begin by roasting the peppers and beets: Preheat the oven to 350 degrees. Wrap each beet in foil and place them on a baking dish along with the peppers. Bake them for one hour. Then, remove the skin and seeds from the peppers. Under running water, rub the skins off the beets. Cut the beets in half and set aside.
Place the peppers in a food processor. Add the feta, garlic, olive oil, and lemon juice. Process the mixture until everything is combined and smooth. Pour in a bowl and top with the pepper flakes and thyme.