3/4 cup (1 1/2 sticks) plus 1 tablespoon unsalted butter, room temperature
4 tablespoons cream of coconut or unsalted butter
2 teaspoons pure coconut extract
2 cups all-purpose flour, plus more for work surface
1/2 teaspoon coarse salt
1 large egg white, lightly beaten
Process nuts and 2 tablespoons sugar in a food processor until finely ground; set aside. Process 1 cup coconut until coarsely ground; set aside.
Put butter, cream of coconut, and remaining 3/4 cup sugar in the bowl of an electric mixer fitted with the paddle attachment; beat on medium until pale and fluffy, about 2 minutes. Mix in coconut extract. Reduce speed to low. Add flour, salt, nut mixture, and ground coconut; mix until combined.
Halve dough. Shape halves into disks, and wrap well in plastic. Refrigerate until firm, about 1 hour.
Let dough soften before rolling. Roll out each disk on lightly floured parchment to 1/4 inch thick. Cover with plastic; refrigerate until firm, 30 minutes.
Preheat oven to 325 degrees. Cut dough into squares using a fluted 2 1/4-inch square cookie cutter. Reroll scraps; continue cutting out squares. Space about 1 inch apart on baking sheets lined with parchment. Lightly brush tops with beaten egg white; sprinkle with remaining 1/2 cup coconut. Bake until golden, 20 to 25 minutes, rotating sheets halfway through. Let cool on sheets on wire racks. Cookies can be stored in airtight containers at room temperature up to 1 week.
To toast macadamias, place them in a single layer on a rimmed baking sheet in a 350-degree oven until lightly golden, about 10 minutes, stirring occasionally.