Line a 9-by-5-inch loaf pan with parchment to overhang the edges and set aside. Carefully remove the coconut milk cans from the refrigerator so the fat and liquid remain separated. Spoon the hardened coconut cream from the can and place in a large bowl (save the liquid for another use, such as smoothies).
Beat the coconut cream in a medium bowl with an electric mixer on high speed until fluffy and medium peaks form. Reduce the speed to low and add the confectioners’ sugar, vanilla, ground ginger, zest of 1/2 lime and salt and beat until just combined. Gently fold in the crystalized ginger with a rubber spatula.
Place 8 of the Gingersnap Cookies in an even layer on the bottom of the prepared loaf pan (they may overlap just slightly and that is okay). Spread a heaping 1/2 cup of the coconut cream mixture on top, then repeat the process 4 more times, ending with the remaining coconut cream on top. Garnish with the zest from the other lime half, the toasted coconut and sprinkles (if using).
Cover and refrigerate until the cookies are completely softened, 6 hours and up to overnight.
Stir together the flour, cinnamon, ginger, baking powder, allspice, baking soda, cloves and salt in a medium bowl. Beat the butter and sugar in a mixer fitted with the paddle attachment on high speed until light, about 1 minute. Scrape down the sides and add the egg and molasses. Beat until well combined. Add the flour mixture and beat on low speed until the dough comes together and cleans the sides of the bowl.
Divide the dough into 2 portions. Lay out a piece of plastic wrap about 16 inches long. Form one portion of the dough into a log and place at one end of the plastic. Roll the plastic around the dough and roll with your hands to make a log about 8 inches long and 1 1/2 inches wide. Twist the ends to seal well. Repeat with the remaining dough. Chill until firm, at least 2 hours. (You can also freeze the dough, using directly from the freezer.)
To bake, preheat the oven to 350 degrees F with a rack in the top and bottom thirds. Line 2 baking sheets with parchment paper.
Remove the plastic from a dough log and cut 1/4-inch-thick rounds (a serrated knife works well), placing them about an inch apart on the baking sheets. Bake, rotating the sheets from top to bottom halfway through, until the cookies are crisp and golden on the bottoms and edges, 10 to 12 minutes. Remove to a rack to cool. Repeat with the remaining dough.