For cookies: In the bowl of a stand mixer fitted with the paddle attachment, beat butter and brown sugar at medium speed until fluffy, 2 to 3 minutes, stopping to scrape sides of bowl. Add egg, beating until well combined. Beat in molasses and vanilla extract until combined.

In medium bowl, whisk together flour, oats, ginger, salt, cinnamon, baking soda, and nutmeg until combined. With mixer on low speed, gradually add flour mixture to butter mixture, beating until combined. Cover and refrigerate for 1 hour.

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

Using a 1½-tablespoon spring-loaded scoop, scoop dough (about 30 grams each), and place 3 inches apart on prepared pans.

Bake until cookies flatten and tops look dry, 10 to 12 minutes. (Do not overbake.) Let cool on pans for 5 minutes. Remove from pans, and let cool completely on wire racks.

For filling: In the bowl of a stand mixer fitted with the paddle attachment, beat butter, vanilla bean paste, and salt at medium speed until combined. Reduce mixer speed to low; gradually add confectioners’ sugar, beating until smooth and well combined, stopping to scrape bottom and sides of bowl. Increase mixer speed to medium-high, and beat until fluffy, 1 to 2 minutes.

Transfer filling to a pastry bag fitted with a ¼-inch French star piping tip (Ateco #862). Pipe about 2 tablespoons (30 grams) filling onto flat side of half of cookies. Place remaining cookies, flat side down, on filling. Store in an airtight container for up to 3 days.