Put the blackberries and tablespoon of sugar into a small saucepan with enough water to just cover the bottom of the pan.

Cook on medium low until the blackberries have broken down, stirring and mashing occasionally.

Pass the blackberries through a sieve over another small saucepan to strain the seeds out from the juice. Use a spatula to mash the blackberries in the sieve to get as much blackberry juice as you can.

Heat the blackberry juice over medium-low heat until it starts to thicken to a maple syrup consistency. Turn off the heat and let cool to room temperature.

Refrigerate if not using immediately.

Preheat the oven to 350°F. Butter an 8 inch or 9 inch square baking pan, or line with foil or parchment paper.

Melt the bittersweet chocolate, unsweetened chocolate, and butter together in a double boiler. Set aside to let cool slightly so it does not cook the eggs when added.

Into a small bowl, sift or whisk together the flour, cocoa powder, and salt.

Put the 1¼ cup of sugar and 3 eggs for the brownie layer into the bowl of your stand mixer or a medium bowl if you are using a hand mixer. Beat the sugar and eggs together until lightened in color.

Beat in the Grand Marnier or vanilla extract.

Add the melted chocolate and butter mixture and mix.

Fold in the dry ingredients (flour, cocoa, and salt) by hand.

Pour or spoon into the prepared pan and smooth. Set aside.

Clean your mixing bowl and beaters.

Add the cream cheese and ¼ cup of sugar to the bowl and beat for a couple of minutes until soft.

Add the egg and vanilla and beat for an additional minute.

Add the tablespoon of flour and salt and beat on low or stir by hand.

Spoon the cheesecake layer on top of the brownie layer and even it out in the pan, being careful not to dig into the brownie layer.

Add spoonfuls of blackberry syrup across the top of the cheesecake layer. You will likely have excess, so don't feel like you have to use it all.

Use a knife to carefully swirl the syrup into the cheesecake layer without going into the brownie layer.

Bake on a rack in the middle of the oven for 45 to 55 minutes. The cheesecake layer will look puffed and set but still moist, and a toothpick inserted down into the brownie layer should come out with just a few crumbs.

Let cool for at least an hour prior to cutting.

Because of the cheesecake layer, these brownies need to be stored, covered, in the refrigerator. They can also be double-wrapped and stored in the freezer for 3 to 6 months.