Combine flour, confectioners' sugar, butter, and egg yolk together in a bowl. Mix until dough is well combined.
Place dough onto a round piece of parchment paper. Roll dough out onto your work surface, rotating the parchment clockwise after each roll, until dough is about 1/10-inch thick. Slide dough and parchment paper into a tart pan and align the edges.
Bake on the lowest rack in the preheated oven until golden brown, about 20 minutes. Remove from oven. Keep oven on.
Whisk 2 pureed persimmons together with ricotta cheese, mascarpone cheese, and honey in a bowl. Spread mixture over the baked dough, leaving 1/4- to 1/2-inch space on the edges.
Place dough back in the oven and bake until a toothpick inserted into the cheesecake comes out clean, 10 to 15 minutes. Remove and let cool in the pan until firm, at least 15 minutes.
Spread the remaining persimmon puree over the cake. Sprinkle blueberries on top.