Preheat oven to 350 degrees with rack in the middle. Butter a 9-inch round cake pan, line bottom with a round of parchment paper then butter the parchment paper, or spray a 13 cup coffee cake pan with non-stick spray with flour.

In a small mixing bowl, combine sour cream and 2 tablespoons of lime juice; set aside.

In a medium mixing bowl, whisk together the flour, baking powder, baking soda, and salt.

Place ½ cup shredded coconut and process in a mini food processor until finely chopped (you can also finely chop it with a knife). Stir the chopped coconut into the flour mixture and set aside.

In a large mixing bowl, beat together butter, sugar, and lime zest with an electric mixer until very fluffy. Beat in eggs, one at a time. Turn mixer to low speed, add one third of the flour mixture, beat well, then beat in half of the sour cream. Beat in another third of flour mixture, then second half of sour cream. End with the last third of the flour mixture, beat until well combined, making sure to scrape down the bowl with a spatula.

Spoon batter into the buttered cake pan and smooth the top with a spatula. Bake in the center of a preheated 350 degree oven until golden and a wooden skewer inserted in the center comes out clean, 35-45 minutes for a 9-inch pan, 20 - 30 minutes for a 13 cup coffee cake pan (an internal temperature of 210 degrees).

Cool for 10 minutes on a wire rack, then turn out of pan and discard parchment if using.

Whisk together powdered sugar and the remaining four tablespoons of lime juice. Poke top of cake all over with a toothpick or fork then pour glaze over the top and drizzle down the sides of the cake, reserving ½ cup.

Pulse the remaining ½ cup coconut and the reserved lime zest in the food processor to coarsely chop it. Sprinkle coconut on top of cake and drizzle remaining glaze over coconut.