Preheat oven to 350 degrees. Grease a 13x9x2-inch baking pan. Combine flour, baking powder, and ¼ teaspoon salt. Melt butter; remove from heat. Stir in sugar. Add eggs and vanilla; stir until combined. Add dry ingredients into sugar mixture. Spread in pan. Bake for 20 to 25 minutes. Cut into bars while warm.