"There are not that many desserts with persimmons. However, they are very healthy and make your desserts delicious and naturally sweet without adding sugar. They will also make the texture of your cheesecakes more sophisticated. The cake is good on the same day or on the next day. If you want to eat it on the next day, keep it in the fridge uncovered. Your cookie pastry is still very soft and fresh. If you cover it, it will become soggy."
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.
You can make it the pastry dough thicker if you like to taste more pastry in your cake. The good thing about sweet pastry dough is that it is like plasticine. If it breaks in one place you can take a piece from another place and fix the gap.
Baking trick: air bubbles might start creating under the dough. To avoid that, you can make a few holes in the dough with a fork or put baking stones on top of the dough.
Do not use a blender in Step 4; ricotta and mascarpone are too fragile and need a bit of air.