Preheat your oven to 325 °F (about 163 °C). Line the 8×8 metal pan with foil or parchment (leave overhang). In a bowl, whisk melted butter, sugar, cocoa powder, and salt until smooth. Let cool slightly, then stir in vanilla, eggs one at a time, then fold in flour until just combined. Spread that batter evenly into the pan, and bake for about 15 minutes—your goal is a just-set top, not fully baked. Chill while you prep the other layers.
Beat the softened cream cheese and sugar until creamy and smooth. Add the eggs one at a time, beating gently after each, then stir in the flour and salt just until combined—avoid overmixing. Pour this cheesecake mixture over the cooled brownie base.
In another bowl, cream together softened butter, brown sugar, granulated sugar, salt, vanilla, and milk. Gradually mix in flour until it forms a soft dough, then fold in the chocolate chips. Roll or press that dough between parchment into an 8-inch square, chill briefly, then place it on top of the cheesecake batter.
Bake the layered pan at 325 °F for about 50 minutes, until the cheesecake is set and the cookie dough is lightly golden. Let cool to room temp, then refrigerate at least 2 hours before cutting.