Cream together the butter and sugar in the bowl of an electric mixer fitted with the paddle attachment at medium low speed until smooth. Add the egg yolk, vanilla, and tangerine zest and mix until combined. Set aside.
In a separate bowl, mix together the flour, almond meal, cinnamon, and salt until blended. Add the flour mixture to the butter mixture and blend until the dough just comes together. Form the dough into two separate balls, cover in plastic wrap, and refrigerate for a minimum of 1 hour and up to overnight.
Preheat the oven to 350 degrees Fahrenheit. Roll out one of the balls of dough until it is 1/4-inch thick. Use your cookie cutter to cut out all the cookie shapes and transfer them to a baking sheet lined with parchment paper. Make sure to cut out an even number of each shape, since you will need two of each shape to make the linzer cookie sandwich.
When the baking sheet is filled with cookies in an even layer, leaving about 1-inch of space between cookies, place the pan in the freezer for 20 minutes. Remove and place it in the oven. Bake until the cookies just begin to turn golden around the edges, about 8 minutes. Remove from the oven and allow to cool for 15 minutes before transferring the cookies to a wire rack to cool completely.
Bring cranberries, sugar, and water to a boil over medium high heat. Reduce heat to medium low, add cinnamon, and stir. Allow to cook until thickened and jammy, about 4 to 7 minutes more. Remove from heat, stir in vanilla extract, and set aside to cool to room temperature. Meanwhile, stir together the mascarpone and powdered sugar in a small bowl until smooth. Stir in the cooled cranberries until combined. Set aside.
Bring water, sugar, and cinnamon stick to a boil in a medium saucepan over medium heat. Add slices in one even layer on top of saucepan, working in batches if necessary. Boil until softened, about 5 minutes per side. Remove and place on a wire rack to cool to room temperature.
Use the cookie cutter to cut the desired shapes out of the persimmon slices. Sandwich the persimmon slices between two linzer cookies. Repeat with half of the linzer cookies. Use a small spoon to spread some of the cranberry mascarpone filling on one of the cookies, then top is with another cookie of the same shape. Repeat with the remaining linzer cookies. Sprinkle all cookies with powdered sugar and serve.