Preheat the oven to 350°F. Grease and flour two 9-inch round cake pans.
In a large mixing bowl, cream 1 cup softened butter and 2 cups granulated sugar until light and fluffy.
Add 4 large eggs to the butter mixture, one at a time, beating well after each addition, then mix in 1 tablespoon vanilla bean paste.
In a separate bowl, whisk together 2 1/2 cups flour, 1 teaspoon baking powder, 1 teaspoon baking soda, and 1/2 teaspoon salt.
Add the dry ingredients to the creamed mixture in batches, alternating with 1 cup buttermilk, beginning and ending with the dry ingredients, mixing just until combined.
Divide the cake batter evenly between the prepared pans and smooth the tops.
Bake the cake layers for 25 to 30 minutes, or until a toothpick inserted in the center comes out clean; leave the oven at 350°F.
While the cake bakes, prepare the cheesecake filling by beating 16 oz softened cream cheese and 1/2 cup granulated sugar in a bowl until smooth.
Beat in 2 large eggs, one at a time, then mix in 2 teaspoons vanilla bean paste and 1/2 cup sour cream until the mixture is smooth and creamy.
When the cake layers are baked, remove them from the oven and carefully pour or spoon the cheesecake mixture evenly over the hot cake in one of the pans, spreading it into an even layer.
Return the cheesecake-topped cake layer to the oven and bake for 15 to 20 minutes, or until the cheesecake is set around the edges and slightly jiggly in the center.
Let both cake layers cool completely in their pans on wire racks, then carefully remove them from the pans.
For the coconut-pecan frosting, combine 1 cup evaporated milk, 1 cup granulated sugar, 3 egg yolks, and 1/2 cup butter in a medium saucepan.
Cook over medium heat, stirring constantly, until the mixture is thickened and coats the back of a spoon.
Remove the pan from heat and stir in 1 teaspoon vanilla bean paste, 1 1/2 cups shredded coconut, and 1 1/2 cups toasted chopped pecans; let the frosting cool until spreadable.
Place the plain white cake layer on a serving plate and top with the cheesecake-centered layer, cheesecake side up.
Spread the cooled coconut-pecan frosting evenly over the top of the cake, letting some drip slightly over the edges.
Slice the cake with a sharp knife and serve.