For the cake: Adjust oven rack to middle position and heat oven to 350 degrees. Grease two 9-inch round cake pans, line with parchment paper, grease parchment, then flour pans. Process coconut in food processor until finely ground, about 1 minute. Combine coconut, buttermilk, and vanilla in 2-cup liquid measuring cup and let sit until coconut is slightly softened, about 10 minutes; reserve.
Combine flour, baking powder, salt, and baking soda in bowl. Using stand mixer fitted with paddle, beat butter, shortening, and sugar on medium-high speed until pale and fluffy, about 3 minutes. Add eggs, one at a time, and beat until combined. Reduce speed to low and add flour mixture in 3 additions, alternating with 2 additions of reserved coconut-buttermilk mixture, scraping down bowl as needed. Add ¾ cup pecans and give batter final stir by hand.
Scrape equal amounts of batter into prepared pans and bake until toothpick inserted in center comes out clean, 28 to 32 minutes. Cool cakes in pans on wire rack for 10 minutes. Remove cakes from pans, discarding parchment, and cool completely, about 2 hours. (Cooled cakes can be wrapped with plastic wrap and stored at room temperature for up to 2 days.).
For the frosting: Using stand mixer fitted with paddle, mix butter and sugar on low speed until combined, about 30 seconds. Increase speed to medium-high and beat until pale and fluffy, about 2 minutes. Add cream of coconut, vanilla, and salt and beat until smooth, about 30 seconds. Add cream cheese, one piece at a time, and beat until incorporated, about 1 minute. Refrigerate until ready to use.
When cakes are cooled, spread 1½ cups frosting over 1 cake round. Top with second cake round and spread remaining frosting evenly over top and sides of cake. Press remaining pecans onto sides of cake. Serve. (Cake can be refrigerated for up to 2 days. Bring to room temperature before serving.).