Make the Cookies:
Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, cream the butter, granulated sugar, and brown sugar until light and fluffy, about 2–3 minutes.
Beat in the egg, vanilla extract, and milk until smooth.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Scoop tablespoon-sized portions of dough onto the prepared baking sheet, spacing them 2 inches apart. Flatten slightly with your fingers or the back of a spoon.
Bake for 10–12 minutes, or until the edges are lightly golden. Cool completely on a wire rack.
Prepare the Ganache:
Heat the heavy cream in a small saucepan or microwave until steaming (but not boiling).
Pour the hot cream over the chocolate chips in a bowl. Let sit for 2 minutes, then stir until smooth and glossy. Let cool slightly to thicken.
Assemble the Cookies:
Spoon or pipe a dollop of vanilla pudding onto the flat side of half the cookies.
Top with the remaining cookies to create sandwiches, pressing gently to secure.
Top with Ganache:
Spoon or drizzle the chocolate ganache over the tops of the assembled cookie sandwiches. Let the ganache set before serving.