Preheat oven to 350°F (175°C). Grease a 9x13-inch baking pan and line with parchment paper for easy removal.

In a large bowl, cream together the softened butter and sugar until light and fluffy, about 3 minutes. Add eggs one at a time, beating well after each addition.

In a separate bowl, whisk together flour, baking powder, salt, and 3/4 cup shredded coconut until evenly distributed.

Combine coconut milk, whole milk, and vanilla extract in a measuring cup. Add the flour mixture and milk mixture to the butter mixture in three alternating additions, beginning and ending with flour. Mix just until combined.

Pour batter into prepared pan and bake for 25-30 minutes, until a toothpick inserted in the center comes out clean. Cool completely in the pan on a wire rack, about 1 hour.

Crumble the cooled cake into fine crumbs in a large bowl using your hands. Add cream cheese frosting and mix thoroughly until the mixture holds together when squeezed but isn't overly wet.

Roll the mixture into 1.5-inch balls (about 2 tablespoons each) and place on a parchment-lined baking sheet. Freeze for 15 minutes to firm up.

Melt white chocolate in a microwave-safe bowl in 30-second intervals, stirring between each, until smooth and fluid. Dip the tip of each lollipop stick into melted chocolate, then insert into a cake ball. Return to the freezer for 10 minutes.

Dip each cake pop into the melted white chocolate, tilting the bowl to fully coat. Tap gently against the bowl edge to remove excess chocolate. Immediately sprinkle with toasted coconut if desired.

Stand the pops upright in a styrofoam block or lay them on parchment paper to set completely, about 15 minutes at room temperature or 5 minutes in the refrigerator.