Preheat oven to 300 degrees F (150 degrees C). Grease and flour an 8x8-inch baking dish.
Beat sugar and butter together until light and fluffy, about 3 minutes; beat in eggs and lime juice. Stir flour and baking powder into butter mixture until combined. Pour batter into prepared baking dish.
Bake in preheated oven until brown and toothpick inserted in center comes out clean, about 25 minutes. Garnish with chopped peanuts.