Preheat the oven to 400°. Place a 10-inch skillet in the oven while it is preheating to keep it warm.
In a large bowl, combine the eggs, flour, sugar, oil, orange juice, and baking powder. Mix all ingredients until smooth using a stand mixer, hand mixer, or whisk.
Place the butter in the skillet while it is warming up in the oven. Take the skillet out of the oven when the butter is fully melted. Make sure the butter is evenly distributed.
Pour the batter into the hot skillet. The batter will be thick, so use a spatula to make sure the batter is evenly distributed in the pan.
Scatter the figs around the top of the cake. Make sure they are evenly distributed.
Place the skillet back in the oven and lower the oven temperature to 350°. Bake for 50-60 minutes. The cake will be golden brown when done.
Let the skillet cool down completely before serving. Store the cake in an air-tight container.