In the bowl of a stand mixer fitted with the paddle attachment, cream the coconut oil and both sugars. Add the eggs and coconut extract. Mix well. Scrape bowl.
Combine the flour, baking powder, and salt in a bowl. Add dry ingredients to wet ingredients. Mix until just incorporated. Spread mixture evenly into a greased 13x9-inch pan.
Bake at 375˚F for 12 to 20 minutes until just baked through. (Baking time depends on the type of pan used.) Do not wait for edges/top to brown. Cool completely.
Make Frosting: In a large bowl, beat the butter and coconut oil until smooth and fluffy with an electric mixer. Add 2 cups of powdered sugar. Mix. Add the remaining 2 cups of powdered sugar, 1 tsp coconut extract, and ¼ cup milk. Spread over cooled bars. Sprinkle with sweetened coconut flakes. Cut into bars, 4 rows by 6 rows (making 24 pieces).