Closely adapted from Samantha Seneviratne.
Preheat the oven to 350 F. Line a 9 inch square baking pan with parchment paper, leaving an overhang on 2 opposite sides.
First prepare the compote by placing the cherries, sugar, spices and salt in a small saucepan. Place them over medium heat and stir occasionally until they start to burst and bubble. When they are quite tender, use a potato masher to smash them. Reduce the heat to simmer.
Remove about 2 tablespoons of the juice and whisk it in a small bowl with the cornstarch. Stir this back into the sour cherries. Continue simmering another 2-5 minutes, stirring occasionally, until the compote has thickened.
Remove the compote from the heat and let it cool for 5 minutes. It should then be the consistency of loose jam; if it is looser than that, simmer an additional minute or two until is. Reserve 1 1/2 cups of this mixture--Seneviratne suggests saving any extra to top vanilla ice cream!
Next make the pastry dough. Add the flour, sugar, baking powder and salt to a food processor fitted with the blade. Pules several times to thoroughly mix.
Add the butter and pulse until the mixture is like coarse meal, with no pieces of butter larger than a pea. Do your best to not over work the dough.
Add the egg yolks and pulse until the mixture is evenly moistened but is still a little sandy.
Dump a little more than half of this into the prepared pan. Using damp hands, press this into the pan evenly. Bake until it is set and golden brown, about 25 minutes.
While the crust is baking, make the cheesecake filling: Using either a whisk or a whisk attachment in a mixer bowl, beat the cream cheese and sugar until it is smooth and creamy and then beat in the egg. Be sure to scrape the sides and bottom of the bowl to mix evenly!
Let the baked crust cool about 5 minutes and then pour the cheesecake mixture evenly over the it. Dollop equal sized spoonfuls of the cherry compute (I used a large soup spoon) evenly over the cheesecake. Using a small offset spatula, spread the compote over the cheesecake layer evenly, doing your best to keep the cheesecake layer on the bottom and the compote on top.
Sprinkle the remaining pastry dough over the compote, squeezing small handfuls of it to form clumpy pieces.
Bake for 30-40 minutes, until the cheesecake layer is set and the top is golden brown. Let it cool completely in the pan before using the parchment overhang to quickly and gently remove it from the pan and onto a cutting board. Slice into squares to serve.
Store bars in the refrigerator.