Preheat the oven to 350 degrees. Grease 2 9 inch round cake pans and line with parchment paper.
Pour four Tablespoons (1/4 cup) of the butter into a frying pan. Add the fresh pineapple and cook over medium heat, stirring occasionally, for about 10 minutes. Remove from heat.
Meanwhile, in a small mixing bowl, sift together the flour, baking powder, and salt. In the bowl of an electric mixer, beat the eggs until smooth and lighter in color. Add the remaining butter, sugar, vanilla, and coconut extract and beat until smooth. Stir in the flour and pineapple along with any juices and butter in the pan. Stir gently to combine.
Divide the batter evenly between the two pans and smooth the top. Bake for 30-35 minutes until cake is browned and toothpick inserted in the center comes out clean. Allow to cool for 5-10 minutes, then run a knife along the edge and invert the cake onto a wire rack to cool completely.