Preheat the oven to 350 F. Line an 8×8 inch square pan with two strips of parchment paper. Leave an overhang on all four sides.
Melt the butter in the microwave until just melted (alternatively, you can melt it over the stove top) Add the chocolate chips and stir until melted. Return to the microwave for a brief time and stir until just melted. Pour into a large mixing bowl.
To the melted butter/chocolate mixture, add the sugars and vanilla. Whisk for one minute. Add the eggs one at a time and whisk for an additional 2 minutes.
Using a wooden spoon or spatula, stir in the flour, baking powder, cocoa powder and salt and mix until combined. Avoid overmixing.
Pour the brownie batter into the pan. Use a spatula or offset spatula to evenly spread the brownies. Top with half the strawberries. Bake the brownies for 30 minutes.
While the brownies bake, prepare the cream cheese topping (see below for instructions).
Remove brownies from oven and carefully spread the cream cheese mixture over the brownies with a spatula or offset spatula. Top with remaining strawberries. Bake for an additional 20 minutes or until the cheesecake is set.
If adding the chocolate on top, remove the brownies from the oven during the last minute of baking. Scatter the chopped chocolate over the top. Bake for an additional 1-2 minutes until the chocolate melts. Remove from the oven.
Allow the brownies to cool in the pan at room temperature then transfer to the refrigerator to cool completely.