Combine the blueberries, sugar and lemon juice in a small saucepan, Cook over medium heat for about 5 minutes, stirring frequently, until the blueberries become soft. Combine the cornstarch and water, mixing until smooth. Stir into the blueberries and bring to a boil. Cook for an additional 2 minutes, stirring continuously. Remove from heat and cool to room temperature. Pour into a blender or food processor, and blend until smooth.
In a food processor or small bowl, add the graham cracker crumbs and sugar. Slowly add the melted butter until completely incorporated. Press onto the bottom of a greased 9-inch round pan. Bake at 350° for 10 minutes. Cool on a wire rack.
In a standing mixer or large bowl, beat the cream cheese and sugar until smooth. Beat in the yogurt, flour, and vanilla. While beating slowing, add the eggs until just combined. Pour over crust. Drizzle with 3 tablespoons of the blueberry mixture. Cut through the batter with a knife or skewer to swirl.
Place the pan on a baking sheet and bake at 350° for 40 minutes, or until the center is almost set. Cool on a wire rack for at least an hour. Refrigerate overnight. When serving, drizzle the remaining blueberry sauce over each slice.
Notes
When making mini-cheesecake, use ramekins and bake for about 25 minutes. Any remaining blueberry sauce can be used on pancakes, waffles, ice cream, and more!