Position a rack in the middle of the oven and preheat to 350 degrees. Grease a 12-cup muffin pan with butter.
Pulse the flour, 1/4 cup coconut, brown sugar and salt in a food processor until combined. Add the cold butter and pulse until the mixture resembles wet sand with pea-sized pieces, about 5 times. Put 1 heaping tablespoon of the mixture in each muffin cup and press to make even rounds. Bake until the crusts are golden, about 20 minutes.
Remove the pan from the oven and sprinkle the chocolate evenly over each crust. Turn off the oven; return the pan to the oven to melt the chocolate, about 3 minutes. Sprinkle each crust with 1 tablespoon of the remaining coconut. Cool slightly, then freeze crusts in the pan until set, about 15 minutes.
With a thin spatula, gently remove each crust from the muffin pan. Top with a small scoop of coconut ice cream, drizzle with dulce de leche and garnish with more coconut.