Preheat the oven to 350°F and bake and cool the gluten-free graham cracker crust in a 9-inch springform pan according to this post (once the pan is cool to the touch, you can speed up cooling the crust by placing it in the fridge). Keep the oven on.

Prepare the blueberry swirl. In a small saucepan, toss the blueberries, granulated sugar, and lemon juice together and cook, stirring occasionally, over medium heat until the blueberries begin to break down and release their juices, 3-5 minutes. Meanwhile, whisk the water and cornstarch together in a small bowl with a fork, creating a slurry. Slowly pour the corn starch slurry into the blueberries, stirring as you pour. Cook for 1-2 minutes longer until the syrup begins to thicken. Remove from heat and pour half of the sauce into a blender or food processor and blend until smooth. Pour into a bowl and chill until no longer warm (speed this up in the freezer, stirring every couple of minutes). Transfer the remaining chunky sauce to a small bowl and chill until ready to serve.

Beat the cream cheese and ¾ cup of the granulated sugar over medium-high speed in the bowl of a stand mixer or a large bowl with a hand mixer, until smooth and creamy, scraping down the sides a few times. Add the sour cream, vanilla, and salt, and beat on medium speed combined, scraping down the sides again.

Mix the remaining 2 tablespoons of sugar with the matcha powder very well, then add it to the filling, mixing on medium speed until just evenly combined, scraping down the sides a couple of times. Add the eggs, one at a time, mixing on medium speed until just combined, scraping down the sides after each addition. Be careful not to overmix the filling after you've added the eggs or you will incorporate too much air into the cheesecake, leading to potential cracks.

Pour the filling into the cooled crust, give it a couple of taps on the counter to release any air bubbles, then use an offset spatula to smooth the top. Use a small spoon to dollop 3 tablespoons of the blueberry purée in random drops over the top of the cheesecake. Use a chopstick, knife, or toothpick to swirl the blueberry purée into the top of the cheesecake, as pictured above. Mix any remaining purée back into the chunky blueberry compote.

Prepare a steaming pan by boiling about 2-quarts of water. Place 9x13 baking dish on the bottom rack of the preheated oven. Place the cheesecake on the middle rack of the oven and pour the boiling water into the 9x13 pan on the bottom rack. Quickly close the oven and bake for 50-60 minutes, checking for doneness around 45 minutes, to account for oven variation. See notes below on how to tell when it's done.

When it's done baking, turn off the oven and open the door a few inches. Let the cheesecake cool in the oven for an hour. Then transfer the cheesecake to the fridge to chill for at least 6 hours or overnight.

Use a thin knife around the outside edge to ensure the cheesecake is loosened from the pan, then release it from the springform pan. Use a clean sharp knife to cut the cheesecake into slices. To make clean slices, I recommend wiping off the knife, then placing it in warm water, and wiping dry before each cut.

Serve slices chilled topped with remaining blueberry compote. Store any leftovers covered in the fridge for up to 5 days or in the freezer for up to 2 months.