Spread the macadamia nuts in a single layer on a rimmed baking sheet.
Toast until lightly golden and fragrant, about 10 minutes.
Let cool, then slice 22 nuts in half.
Finely grind the remaining nuts, and set aside.
In a medium bowl, whisk together flour, baking powder, and salt; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter, shortening, and sugar on medium speed until light and fluffy, 3 to 4 minutes, scraping down the sides of the bowl as needed.
Beat in 2 eggs and the vanilla to combine.
Add the flour mixture, ground macadamia nuts, and coconut; mix on low speed until just incorporated.
Turn out the dough onto a clean work surface.
Shape into an 11-inch log, 2 inches in diameter.
Wrap in plastic, and refrigerate until firm, at least 2 hours or overnight.
Preheat oven to 350F, with racks in the upper and lower thirds.
Line two large baking sheets with parchment paper.
Remove log from refrigerator.
Using a sharp knife, cut into 1/3-inch-thick slices.
Place slices about 1 1/2 inches apart on prepared baking sheets.
In a small bowl, whisk together the remaining egg with 1 tablespoon water.
Using a pastry brush, lightly brush the top of each cookie with egg wash. Sprinkle with coconut, and press a macadamia half into the center.
Bake, rotating sheets halfway through, until the edges are golden and the coconut on top is lightly toasted, 14 to 16 minutes.
Transfer to a wire rack to cool completely.
Cookies can be kept in an airtight container at room temperature for up to 5 days.