To pre-bake the brownie layer:

1. Preheat the oven to 350 degrees and line a square 9 x 9 pan with parchment paper. Alternatively, you can butter the insides of the pan.
2. Add the flour, cocoa powder, espresso powder, baking powder and salt to a small bowl and whisk to combine well. Set aside.
3. In a larger bowl, cream the butter and both sugars together until fluffy, about 2-3 minutes on medium high speed. Scrape down the bowl, add the egg and mix for another 2 minutes. Beat in the milk and vanilla for another minute and scrape down the bowl again.
4. Add the melted chocolate all at once and beat on medium high speed for 2 more minutes. Add the flour/cocoa mixture and mix on low speed for about a minute just until combined.
5. Use a spatula to make sure that there are no unmixed dry ingredients on the bottom of the bowl. If you find any, gently fold them into the rest of the batter.
6. Carefully spread the brownie batter into the prepared pan, using an offset spatula to create an even layer. The batter will be quite thick.
7. Bake the brownie layer for 16-17 minutes, until it has mostly set. It will not be done in the middle, that’s okay. Right after putting the pan into the oven, make the cheesecake filling so that it is ready right when the brownie layer is done baking.

To make the cheesecake filling and bake the bars:

1. Add the cream cheese, sugar, crème fraiche, flour and salt to the bowl of a food processor. Pulse for a few seconds to blend everything together.
2. Scrape down the sides of the bowl with a spatula and add one egg. Pulse for a few seconds to blend. Scrape down the bowl again and add the remaining egg, Irish cream and vanilla. Pulse for a few seconds more until the filling is well blended and smooth. Set aside the filling until the brownie layer comes out of the oven.
3. After the brownie layer comes out of the oven, carefully and slowly pour the cheesecake filling over the top, beginning with the edges and working your way into the center. Don’t hold the bowl of filling more than a few inches above the brownie as you pour it. Spread the cheesecake filling into an even layer.
4. Bake the layers at 350 degrees for 40-45 minutes, or until the center is only slightly jiggly and the edges are set. Allow to cool completely to room temperature before chilling overnight.

Make the ganache topping:

1. Add the chopped chocolate to a heatproof bowl and set aside.
2. Combine the heavy cream and corn syrup in a small saucepan and heat over medium until it just before it simmers, stirring occasionally.
3. Pour the hot cream over the chopped chocolate and allow it to stand for one minute. Whisk the chocolate and cream to combine well until smooth.
4. Pour the ganache over the cheesecake bars and smooth into an even layer. Allow the ganache to set in the fridge for at least a half hour before slicing and serving.
5. These bars will keep in the fridge for up to a week. Store them in an airtight container.