In a heavy 10" frying pan with an ovenproof handle, melt butter over medium heat. Add brown sugar and cook, stirring constantly, for about 10 minutes, being careful that it doesn't burn. Drain apricots and reserve 1/4 cup of the syrup. Place apricot halves, cut side up, in a single layer as close as possible to each other over brown sugar in skillet; set aside to cool. In a small bowl, combine flour, baking powder, and salt; set aside. In another bowl, beat eggs with granulated sugar until light and fluffy, stir in 1/4 cup syrup. Gently fold dry ingredients into egg mixture and pour over apricots. Bake uncovered at 350 deg for 35-40 minutes until tooth pick inserted comes out clean. Immediately loosen cake with a spatula and invert onto serving platter. Let skillet rest briefly on inverted cake to allow syrup to drizzle over cake. Serve warm with French vanilla ice cream. If cooked ahead of time, warm briefly in microwave or oven.