Heat the oven to 325 F. Line a 9-inch square baking pan with parchment paper.
Stir the graham cracker crumbs, melted butter, and 2 tablespoons brown sugar together. Press the mixture firmly into the pan and bake for 9 minutes, then cool briefly.
Blend the cottage cheese and Greek yogurt until completely smooth. Add the maple syrup, eggs, cornstarch, vanilla extract, and salt, then blend just until incorporated.
Stir the 1/4 cup brown sugar, cinnamon, and melted butter together to make a thick cinnamon paste.
Pour half of the cheesecake filling over the crust and drizzle with half of the cinnamon paste. Add the remaining filling, then spoon the remaining cinnamon paste over the top and gently swirl it through the surface.
Bake for 45 to 52 minutes, until the edges are set and the center has a slight wobble. Cool completely at room temperature.
Refrigerate the cheesecake for at least 5 hours before lifting it from the pan and portioning it into bars.