Line two baking sheets with parchment paper and set aside.
In a large bowl (or the bowl of a stand mixer) cream 12 tablespoons unsalted butter, softened, with a hand mixer or paddle attachment until light and fluffy.
Add 2 large eggs and 1 teaspoon vanilla extract to the butter and mix until combined.
In a medium bowl, whisk together 2¼ cups all-purpose flour, ¾ cup powdered sugar, ¼ teaspoon baking powder, and ¼ teaspoon kosher salt.
Gradually add the dry mixture to the butter mixture and mix on low speed until the dough just comes together.
Lightly flour your work surface. Turn the dough out onto the floured surface and knead briefly by hand until smooth and uniform.
Using a floured rolling pin, roll the dough to about 1/4 inch thickness.
Use a small round cookie cutter to cut out an even number of cookies. Transfer the cut cookies to the prepared baking sheets, spacing them about 1 inch apart.
Chill the prepared cookie rounds on the baking sheets in the refrigerator for 30 minutes. While they chill, preheat your oven to 350°F.
Bake the chilled cookies at 350°F for 15–18 minutes, or until the edges are lightly golden. Remove from the oven and cool completely on a wire rack before assembling.
Make the chocolate filling: place ¾ cup semi-sweet chocolate chips and 1 tablespoon unsalted butter in a microwave-safe bowl. Microwave in 20-second intervals, stirring between intervals, until smooth and fully melted. Let cool slightly until spreadable.
Spread a thin layer of the melted semi-sweet chocolate onto the flat side of half of the cooled cookies. Top each with a remaining cookie to form a sandwich. Press gently to seal.
Place the sandwich cookies on a baking sheet and refrigerate or leave at room temperature until the semi-sweet chocolate filling is set (about 10–15 minutes).
Melt the white chocolate coating: place 2½ cups white chocolate candy coating in a microwave-safe bowl and microwave in 20-second intervals, stirring between intervals, until smooth and fully melted.
If using the optional colored candy coating (½ cup), melt it in a separate microwave-safe bowl in 20-second intervals until smooth. Transfer the melted colored coating to a small piping bag or a resealable plastic bag and snip a tiny corner for drizzling.
Dip each sandwich cookie into the melted white chocolate coating (or spoon the coating over the top), letting excess drip off, and return to parchment-lined baking sheets.
Immediately drizzle the melted colored candy coating over the white-coated cookies, if using.
Allow the coatings to set completely at room temperature or speed up setting in the refrigerator. Once set, dust the cookies with additional powdered sugar, if desired.