Stir together first 6 ingredients in a large bowl. Stir together 1 cup coffee, coconut milk, oil, flavorings, and eggs; add to dry ingredients. Beat at medium speed with an electric mixer until blended. Pour batter into 2 greased and floured 9-inch round cakepans.
Bake at 350° for 20 to 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on wire racks 10 minutes; remove from pans, and cool on wire racks.
Microwave white chocolate morsels in a large glass bowl at HIGH 1 1/2 minutes or until melted, stirring twice. Add yogurt and 1 tablespoon coffee. Beat at medium speed 30 seconds or until spreading consistency. Spread frosting between layers and on top and sides of cake. Garnish, if desired. Store in refrigerator.
Tip: Bake layers on the center oven rack, and stagger pans for even baking, being careful not to let pan sides touch. Make sure to use unsweetened coconut milk and not cream of coconut.