For the topping, combine blueberries and honey in a small saucepan over medium heat. Once it comes to a boil, reduce to a simmer and cook for 5 minutes with frequent stirring. Add lemon juice and simmer for another 3 minutes. Combine corn starch with water to make a slurry and add to the blueberry mixture. Stir it in and simmer for just 20 seconds until thickened. Pour it out into a clean bowl and set aside to cool.
Preheat the oven to 350°F. Line an 8x8 pan with foil or parchment paper, allowing the ends to extend over the sides.
For the crust, combine flour, brown sugar, cinnamon and salt in a medium bowl and press out any lumps of brown sugar. Add the melted butter and mix well until evenly combined. Press the mixture evenly into the bottom of the prepared pan. Bake 10-12 minutes until lightly golden. Reduce oven temperature to 325°F.
In a medium bowl, beat together cream cheese and sugar until smooth. Beat in egg, then the yogurt and vanilla. Mix melted white chocolate. Place spoonfuls of cooled blueberry compote over the batter and swirl it through with a knife.
Pour the batter over the crust and bake for about 25 minutes until the center is just set with a slight wobble. Let cool completely and then refrigerate for at least 2 hours before slicing.