Preheat oven to 350°F (180°C). Line 2 baking sheets with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter, granulated sugar, and vanilla at medium speed until fluffy, 2 to 3 minutes, stopping to scrape sides of bowl. Beat in egg and molasses until well combined.
In a medium bowl, whisk together flour, baking soda, ginger, cardamom, cinnamon, cloves, pepper, and salt. With mixer on low speed, gradually add flour mixture to butter mixture, beating until well combined. Evenly divide dough into 12 portions (about 55 grams each). Shape each into a ball, and roll in sparkling sugar. Place 2½ inches apart on prepared pans.
Bake until bottoms are golden brown, about 12 minutes. Let cool completely on wire racks.
To assemble, scoop ⅓ cup ice cream on flat side of one cookie. Top with a second cookie, flat side down, pressing gently to spread ice cream to edges. If desired, roll edges of cookies in additional sparkling sugar. Place on a baking sheet and store in freezer. Repeat with remaining cookies and ice cream. Freeze ice cream sandwiches until ready to serve. To store longer, wrap sandwiches individually in plastic wrap and freeze for up to 3 months.
Notes
Pro Tip: To form evenly shaped and measured ice cream portions, line a ⅓-cup dry measuring cup with plastic wrap, letting excess extend over sides. Fill lined measuring cup with slightly softened ice cream. Using excess plastic wrap, lift ice cream out of measuring cup, and invert it onto the flat side of cookies.
Recipe by Bake from Scratch at https://staging.bakefromscratch.com/gingerbread-chai-ice-cream-sandwiches/