Step 1Heat the oven to 350 degrees. Position a rack in the middle of the oven and line two baking sheets with parchment paper.
Step 2Melt the shortening in a small saucepan over medium heat or in the microwave. Measure one-half cup and cool until it reaches room temperature and is slightly thickened. Discard any remaining shortening.
Step 3In the bowl of a stand mixture using the paddle attachment, or in a large bowl using a hand mixer, beat the cooled shortening, molasses, granulated sugar and egg at medium speed until fully incorporated, about 3 minutes (it will not be fluffy).
Step 4Meanwhile, in a medium bowl sift together the flour, baking soda, cinnamon, cloves, ginger and salt. Mix in the combined dry ingredients, one-half at a time, until thoroughly combined, scraping down the sides of the bowl as needed. Divide the dough in half and wrap tightly in plastic. Chill the dough for about 15 minutes to firm slightly.
Step 5Remove half of the chilled dough and roll it out between two sheets of plastic wrap or parchment paper until it is slightly thicker than one-eighth inch thick. Use a 2 1/2 -inch cookie cutter to cut as many cookies as possible from the dough. Peel away the scraps, then gently peel off the cookies. The dough may need to be chilled again to make peeling easier; if so, simply place the dough, still on parchment or plastic, on a baking sheet and freeze for several minutes. Place the cookies 2 inches apart on a parchment-lined baking sheet. Repeat using the rest of the dough and scraps.
Step 6Just before baking, brush the dough rounds lightly with the cream, using a pastry brush. Sprinkle with the coarse sugar.
Step 7Bake the cookies, one pan at a time, until they puff and begin to deflate, and are just beginning to brown, 8 to 10 minutes. Rotate the pan halfway through for even baking. Cool completely on the baking sheets; the cookies will flatten and crack slightly as they cool. Make sure the cookies are completely cool prior to assembly.
Step 8To assemble, spread a heaping one-third cup ice cream (slightly softened) over the bottom of one cookie, and carefully top with another cookie. Press firmly but gently to avoid breaking the cookies. Run a knife or offset spatula around the edges to clean up any ice cream hanging over the edge. Freeze for at least 1 hour to firm the ice cream. Repeat with all the cookies.