Preheat a non-stick skillet over medium heat. Toss the figs in the butter and sprinkle with brown sugar. Place the figs in the pan, cut side down. Cook for 2 to 3 minutes or until golden brown. Turn the figs. Remove the pan from the heat and let stand for 2 minutes.
When serving, spoon the yogurt on the plates with an ice cream scoop. Lay the figs on the yogurt mound and drizzle with honey.