Have all ingredients at room temperature, 68°F to 70°F. Preheat oven to 350°F. Grease and flour two 8 x 2-inch round pans, or one 10- to 12-cup fluted tube or Bundt pan, or line bottoms of round pans with waxed or parchment paper.
Measure cake flour on a sheet of waxed paper. Combine buttermilk, baking soda and vanilla in bowl. In a large bowl, beat butter until creamy, about 30 seconds. Gradually add 1-1/3 cups sugar and beat on high speed until lightened in color and texture, 4 to 6 minutes. Beat in egg yolks, one at a time.
Add the flour in 3 parts, alternating with the buttermilk mixture in 2 parts, beating on low speed or stirring with a rubber spatula until smooth and scraping the sides of the bowl as necessary. Stir in coconut and pecans.
In a medium-sized bowl, beat egg whites and cream of tartar on medium speed until soft peaks form. Gradually add 1/4 cup sugar, beating on high speed. Beat until peaks are stiff but not dry.
Use a rubber spatula to fold one-quarter of the egg whites into the buttermilk batter, then fold in the remaining whites. Scrape the batter into the pan(s) and spread evenly. Bake at 350°F until toothpick inserted in center comes out clean, 30 to 35 minutes in round pans, 55 to 65 minutes in fluted tube or Bundt pan.
Let cool in pan(s) on rack for 10 minutes. Slide a slim knife around the cake(s) to detach it from the pans, or tap the sides of the fluted tube or Bundt pan against the side of the counter to loosen the cake. Invert the cake(s) and peel off the paper liners, if using. Let cool, right side up or inverted, on the rack.
If using 2 round cakes, place one cake layer on platter with waxed paper strips tucked underneath. Use a large dollop of frosting to fill cake; place second layer on top and frost whole cake. If using fluted tube or Bundt cake, place cake on platter with waxed strips; frost whole cake. If desired, garnish cake with toasted coconut. Remove waxed strips and serve.
Have cream cheese cold and butter at room temperature. In large bowl, beat cream cheese, butter and vanilla until just blended. Add powdered sugar in 3 parts and beat until just smooth and the desired consistency. If the frosting is too stiff, beat a few seconds longer. Do not overbeat.