To make cake: Place oven rack in bottom third of oven; heat oven to 350 degrees. Spray two 8-inch cake pans with nonstick cooking spray. Line bottom of each pan with a circle of parchment paper, spray the paper and dust inside of each pan with all-purpose flour, tapping out excess.
Sift together cake flour, baking powder and salt; set aside.
In bowl of electric mixer with paddle attachment, cream butter at medium speed until soft and light. Add sugar and continue to mix about 5 minutes or until light and fluffy. Add egg yolks one at a time, beating after each addition until completely mixed.
On low speed, alternately add flour mixture in 3 additions and coconut milk in 2 additions, beginning and ending with flour mixture. Add extract and beat at low speed until completely mixed.
In clean bowl with whisk attachment, beat egg whites at high speed to soft peaks. Gently fold one third of the egg whites into the batter; fold in remaining egg whites gently but thoroughly. Divide batter between prepared cake pans and bake about 35 minutes or until cake springs back when touched and toothpick inserted into center comes out clean.
Cool on rack 5 minutes; run a small knife around edge of each pan and carefully invert cake onto rack. Remove pan and cool cake completely; remove paper before assembling cake.
To make icing: In small saucepan combine sugar, water and cream of tartar. Bring to a boil, covered, over medium heat; do not stir. When sugar is completely dissolved, uncover and boil 5 minutes longer.
In bowl of electric mixer with whisk attachment, beat egg whites at high speed to soft peaks. Continue to beat while slowly pouring hot syrup onto egg whites; add extract and beat until cool.
To assemble cake: Spread 1/4 cup of the preserves on top of 1 cake layer. Thinly slice 2 cups of the strawberries and arrange in 1 layer on top of preserves. Spread remaining 1/4 cup preserves on bottom of second cake layer and invert onto first layer. Spread icing on top and sides of assembled layers; pat coconut onto sides of cake. Arrange remaining strawberries on top of cake, stem side down.
Tips: Substitute white cake made from a mix; add 1/2 teaspoon of coconut extract to batter. Substitute pre-made white frosting; add coconut extract to taste.