Make the dough. Whisk together flour, cocoa powder, baking soda, and salt in a medium bowl. In a large bowl, beat softened butter and both sugars until light and fluffy, about 3 minutes. Add the egg, egg yolk, and vanilla, mixing well. Gradually fold in the dry ingredients until just combined, then stir in the chocolate chips.

Chill the dough. Wrap the dough tightly in plastic wrap and refrigerate for at least 1 hour (up to 48 hours).

Preheat oven to 350°F. Line two baking sheets with parchment paper.

Scoop and bake. Roll dough into 1-inch balls and place 2 inches apart on prepared baking sheets. Gently flatten each ball slightly with the bottom of a glass. Bake for 9–11 minutes until set at the edges but still soft in the center. Cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.

Make the ganache. Place finely chopped milk chocolate in a heatproof bowl. Heat heavy cream in a small saucepan over medium-low heat until just simmering. Pour over the chocolate and let sit for 1 minute. Stir gently until smooth, then add the butter and a pinch of salt. Let cool at room temperature for 25–30 minutes until thick and spreadable.

Assemble the cookies. Match cookies into pairs of similar size. Pipe or spoon about 1½ teaspoon of ganache onto the flat side of one cookie. Press its partner on top, flat side down, and squeeze gently until the filling just reaches the edges.

Set and serve. Allow assembled cookies to sit for 15 minutes to let the ganache firm up before serving.