2¼ cups (11¼ ounces) unbleached all-purpose flour
½ teaspoon baking soda
1 teaspoon baking powder
½ teaspoon table salt
½ cup sweetened shredded coconut, chopped fine
1 teaspoon finely grated lime zest
1½ cups (10½ ounces) sugar, plus ⅓ cup for rolling
2 ounces cream cheese, cut into 8 pieces
6 tablespoons (¾ stick) unsalted butter, melted and still warm
⅓ cup vegetable oil
1 large egg
1 tablespoon milk
1 tablespoon lime juice
Adjust oven rack to middle position and heat oven to 350º F. Line 2 large rimmed baking sheets with parchment paper or Silpat. Whisk flour, baking soda, baking powder, salt, and shredded coconut together in medium bowl. Set aside.
Place 1½ cups sugar and cream cheese in large bowl. Place remaining ⅓ cup sugar in shallow baking dish or pie plate and set aside. Pour warm butter over sugar and cream cheese and whisk to combine (some small lumps of cream cheese will remain but will smooth out later). Whisk in oil until incorporated. Add egg, milk, and lime juice; continue to whisk until smooth. Add flour mixture and mix with rubber spatula until soft homogeneous dough forms.
Divide dough into 24 equal pieces, about 2 tablespoons each. Using hands, roll dough into balls. Working in batches, roll balls in reserved sugar to coat and evenly space on prepared baking sheet, 12 dough balls per sheet. Using bottom of drinking glass, flatten dough balls until 2 inches in diameter. Sprinkle tops evenly with 4 teaspoons of sugar remaining in shallow dish )2 teaspoons per tray), discarding any remaining sugar.
Bake, 1 tray at a time, until edges are set and just beginning to brown, 11 to 13 minutes, rotating tray after 7 minutes. Cool cookies on baking sheets 5 minutes. Using wide metal spatula, transfer cookies to wire rack and cool to room temperature.