Combine blueberry compote ingredients in a medium pot and bring to a simmer, stirring occasionally.
Simmer for 3-5 minutes, transfer to an airtight container, and refrigerate for at least 30 minutes to cool.
Once cool, pour 2/3 of the mixture into a blender and blend until smooth. If you want more blueberries versus puree in the bars, then puree only half of the compote.
To Make the Graham Cracker Crust
Preheat oven to 325 degrees and line an 8x8 pan with parchment paper to make a sling.
Combine the graham cracker crust ingredients in a bowl and stir until all of the graham cracker crumbs are moist.
Pour the crust mixture into the pan and press the crust down with the back of a measuring cup until smooth and even. Bake for 8-9 minutes, and let cool completely (approx. 30 minutes).
To Make the Blueberry Lime Cheesecake Filling
Cream the cream cheese, Greek yogurt, lime juice, zest, vanilla, and salt in a stand mixer or with a hand mixer until smooth and creamy.
Next, add the powdered sugar and mix until smooth
In a separate bowl, whip the heavy cream to stiff peaks. Then fold the heavy cream into the cream cheese.
Spoon half of the mixture into the pan and smooth out. Add half of the blueberry mixture to the cheesecake and gently mix into the cheesecake.
Pour the remaining cheesecake filling on top and gently smooth out until even. Add the remaining blueberry compote on top and spread until covering the entire surface. Alternately, spoon small amounts of the blueberry mixture on top and swirl into the cheesecake.
Refrigerate the cheesecake for at least 6 hours so that it sets up properly. For easier cutting, chill the cheesecake for 30 minutes in the freezer, and you will get really clean slices every time.
After slicing, store the bars in an airtight container in the fridge for up to a week.