In a medium saucepan, melt butter over medium heat. Cook, stirring frequently, until butter solids are golden and nutty in aroma, 7 to 12 minutes. Pour ¾ cup (139 grams) browned butter into a medium shallow baking dish or bowl. Pour remaining ½ cup (94 grams) browned butter into another medium shallow baking dish or bowl, reserving for Whiskey Buttercream. (See Note.) Refrigerate both until browned butter is solid, 2 to 3 hours. Let stand at room temperature until softened before using, about 30 minutes.

In a small microwave-safe bowl, combine cherries and ¼ cup (52 grams) whiskey; heat on high until hot, about 2 minutes. Let stand for at least 30 minutes, stirring occasionally. Drain cherries.

In the bowl of a stand mixer fitted with the paddle attachment, beat ¾ cup (139 grams) browned butter at medium speed until creamy, 30 seconds to 1 minute; scrape sides of bowl. Add sugars, and beat until fluffy, about 2 minutes, stopping to scrape sides of bowl. Beat in egg, vanilla, and remaining 1½ teaspoons (6.5 grams) whiskey until well combined.

In a medium bowl, whisk together flour, cornstarch, salt, baking powder, and baking soda. Add flour mixture to butter mixture all at once, and beat at low speed just until combined. Fold in cherries and chocolate. Cover and refrigerate for 1 hour.

Preheat oven to 350°F (180°C). Line 2 large rimmed baking sheets with parchment paper.

Using a 1½-tablespoon spring-loaded scoop, scoop dough, and roll into balls (about 28 grams each). Place 1½ to 2 inches apart on prepared pans.

Bake until light golden brown, about 10 minutes. (Cookies may still seem slightly underdone in centers but will set up as they cool; any warm cookies can be formed right out of the oven into a more circular shape, if desired. Using an offset spatula, gently press and curve uneven edges of still-warm cookies.) Let cool on pans for 5 minutes. Remove from pans, and let cool completely on wire racks.

Spoon Whiskey Buttercream into a large pastry bag fitted with a medium open star tip (Wilton 1M). Pipe buttercream onto flat side of half of cookies. Place remaining cookies, flat side down, on top of buttercream. Serve immediately.