Like other caramelized vegetables, sweet potatoes should be cut into thick slices to keep them from getting too soft.
Heat oil in a large skillet over medium heat. Add sweet potatoes; cook, turning occasionally, 3 minutes. Add garlic; cook, stirring constantly, 1 minute. Add wine and stock; simmer, stirring occasionally, until almost all liquid has evaporated, about 20 minutes. Add brown sugar and salt; cook, carefully turning potatoes to brown both sides, about 20 minutes. Transfer caramelized sweet potatoes to a plate. Let cool slightly.