In a large mixing bowl or the bowl of an electric mixer fitted with the paddle attachment, cream the butter, brown sugar, granulated sugar, vanilla extract, and salt on medium speed until light and fluffy. Scrape down the sides of the bowl.
Add the egg yolk and mix again until fully incorporated. Scrape down the sides of the mixing bowl as needed.
Reduce the mixer to low speed and gradually add the flour. Mix just until combined.
Stir in 1 ½ cups of the mini chocolate chips on low speed or by hand.
Divide the dough in half. Roll one portion of dough between two sheets of plastic wrap or wax paper to ¼ inch thickness. Repeat with the other piece. Chill for about 1 hour, or uo to 48 hours.
Preheat the oven to 350°F. Line baking sheets with parchment paper.
Cut into shapes using cookie cutters. Transfer cookies to prepared baking sheets.
Bake for 12–18 minutes, or until the edges and centers are set.
Once the cookies are completely cooled, melt the reserved ½ cup of mini chocolate chips in a microwave. Heat in 20–30 second intervals, stirring between each round, until smooth. Drizzle the melted chocolate over the cookies using a spoon a small zip-top bag with a tiny corner cut off. Let the chocolate set at room temperature before serving or storing.