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Combine all the dry ingredients (1½ cups flour, 1/2 cup powdered sugar, 1/2 tsp salt) in a large bowl.
Slice 1 stick cold butter into to the flour. Keep cutting until the chunks are about the size of a pea (or add everything to the blender and pulse until the chunks are pea-size).
Add 1 egg and mix the ingredients together with a spoon. If using the blender, add the egg and process until the dough starts to stick together.
Use your hands to kneed the dough until it barely starts to come together. Push the dough into a ball (it will be very crumbly, but that’s ok). Cover with plastic wrap. Flatten to make a disk.
Refrigerate for about 1 hour. (Prepare the pears during this time).
Remove the dough from the refrigerator. Shape it into a ball and roll it out between 2 layers of parchment paper or saran wrap, to about 3-4 mm thick (you could just flour your work surface really well and not use the parchment). Transfer into the 12 inch tart mold and pat it with your fingertips to fit it tightly inside the mold. Prick the dough with a fork.
Refrigerate for 30 minutes or freeze for 15 minutes.
Preheat the oven to 300F and bake the tart for about 15-20 minutes.
Let cool on wire rack.
In a large pot combine, 1 cup sugar, 3 cups water, 2 tbsp lemon juice, 5 tbsp vanilla extract, 1 star anise, 1/2 cup alcohol and 1 cinnamon quill. Bring to a boil.
Place the peels & cored pears into the syrup and simmer for about 30 minutes. Let cool (I left the pears in the syrup overnight, which allowed the pears to be completely infused with vanilla).
Once cool, remove pears from the syrup and and slice them thinly.
You can use either blanched or unblanched almond (with the dark part of the nut on or off).
Put 3/4 cup almonds and 2 tsp flour into the bowl of a food processor and grind.
In a bowl of an electric mixer beat, 125 g softened/room temperature butter and 1/2 cup sugar.
Add 2 eggs one at a time and mix well between each addition.
Add the ground up almond mixture. Mix until well combined.
Spoon the frangipane mixture into the tart and spread it around.
Place the thinly sliced pears on top of the frangipane, making a circle, leaving about an inch space from the tarts edge.
Sprinkle sliced almonds around the edge of the tart.
Bake for additional 45 minutes, at 300F.
Remove from the oven and let cool before serving.
While the tart is baking, reduce the leftover syrup/poaching liquid, until thickened (almost like honey).
Brush the tart with this syrup as soon as it comes out of the oven.