Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a bowl, whisk together the flour, baking powder, and salt.
In a separate bowl, cream together the softened butter and sugar until light and fluffy.
Add the eggs and vanilla extract to the butter mixture and mix until smooth.
Gradually add the dry ingredients to the wet mixture, stirring until a soft cookie dough forms.
If the dough feels dry, add a splash of milk to reach the right consistency.
Scoop or drop portions of dough onto the prepared baking sheet, spacing them apart.
Press a small indentation into the center of each cookie to make room for filling.
Bake until the edges are just lightly golden, then let the cookies cool completely.
While the cookies cool, whisk together the instant vanilla pudding mix and cold milk until thickened to make the creamy filling.
Heat the heavy cream until it begins to simmer, then pour it over the chocolate and let it sit briefly before stirring until smooth to make the ganache.
Spoon or pipe the vanilla cream into the cookie indentations.
Drizzle or spoon the chocolate ganache over the filled cookies, letting some drip down the sides.
Chill the assembled cookies until the chocolate sets before serving.