Place a rack in the center of the oven and preheat to 375°F. Line a standard 12-cup muffin pan with paper liners, then lightly mist the liners with nonstick spray.

In a large mixing bowl, combine the 2/3 cup granulated sugar and 1 tablespoon lime zest. Rub the zest into the sugar with your fingertips for about 30 seconds until fragrant.

Whisk in the flour, baking powder, salt, and shredded coconut until evenly mixed.

In a separate medium bowl, whisk the eggs until smooth. Add coconut milk, oil, Greek yogurt, lime juice, vanilla extract, and coconut extract. Whisk until creamy and smooth.

Pour the wet ingredients into the dry ingredients. Fold the batter gently until no dry pockets of flour remain. Let it rest for 5 minutes.

Divide the batter among the muffin cups, filling each about three-quarters full. Mix the shredded coconut and turbinado sugar, and sprinkle it over the muffin tops.

Bake for 18 to 21 minutes or until golden and a toothpick comes out clean. Let cool in the pan for 5 minutes, then transfer to a wire rack to cool for at least 15 minutes.

For the glaze, whisk together the powdered sugar, lime juice, coconut milk, lime zest, and salt until smooth. Drizzle over cooled muffins and let sit for 10 minutes.