Make the cookies: Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper; set aside. Whisk the flour, cinnamon, ginger, cloves and salt in a medium bowl. Beat the butter, granulated sugar and brown sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Add the egg yolk and vanilla and beat until well combined, then beat in the carrots and walnuts. Reduce the mixer speed to low and beat in the flour mixture until just combined.
Roll tablespoonfuls of dough into balls, then roll in the coconut. Arrange 1 inch apart on the prepared baking sheets. Make a deep indentation in the centers with the handle of a wooden spoon. Bake, switching the pans halfway through, until the cookies are set and the coconut is golden brown, 22 to 25 minutes. Let cool completely on the pans.
Meanwhile, make the filling: Beat the cream cheese, butter and vanilla in a medium bowl with a whisk until light and fluffy. Mix in the confectioners' sugar until fluffy. Refrigerate until ready to use. Transfer the filling to a resealable plastic bag. Snip a corner and pipe the filling into the indentation of each cookie. Top with jelly beans.