Beat the butter (10 tablespoons), sugar (1 cup), and vanilla (1/2 teaspoon) with an electric mixer until light and creamy.
Add the egg (2) and beat well.
In another mixing bowl, whisk together the all-purpose flour (1 cup) and self-rising flour (1 cup). Gradually add to the butter mixture and beat just until combined.
Fold in coconut (1 cup) and white chocolate chips (2/3 cup).
With a large cookie/ice cream scoop, scoop out the dough and arrange it on a baking tray lined with parchment paper or Silpat silicone liner. Leave 2" space between each cookie to allow for cookies to spread. Bake for 10 to 14 minutes or until the bottom of the cookie is lightly golden. The top and edges of the cookie will not turn golden. Allow it to cool on baking trays for 15 minutes then remove to a wire rack to cool completely.