Add the powdered sugar and 10 tablespoons of butter to a large bowl. Cream these together using an electric mixer or a stand mixer for about 3 to 4 minutes, until light and fluffy.
Add 1 egg and ½ teaspoon of vanilla extract to the bowl and mix until combined.
Gradually add 2 cups of flour to the bowl and combine with the mixer on low until all the flour is just combined.
Form a ball with the dough, wrap it in plastic wrap, and refrigerate for at least 1 hour.
Once chilled, roll the dough out to ¼-inch thick and slightly larger than the tart pan you are using. Press the dough evenly into the tart pan and trim the excess dough from the edges of the pan. Refrigerate the dough in the pan for 30 minutes or freeze it for 15 minutes.
Preheat the oven to 350 F. Once the dough is chilled in the pan, bake it in the preheated oven for 15 to 20 minutes until the dough feels dry. Remove from the oven.
Add the granulated sugar and the remaining 8 tablespoons of butter to a large bowl. Beat with an electric mixer or stand mixer until creamy.
Add ⅓ of the almond flour and 1 egg to the bowl and beat on low speed, alternate adding the remaining almond flour and remaining 2 eggs until the ingredients are combined evenly.
Add in the remaining tablespoon of all-purpose flour, lemon zest, and the remaining teaspoon of vanilla extract and mix until just combined.
Spread the almond filling evenly in the baked tart shell. Arrange the sliced apricots over the almond filling and then sprinkle the sliced almonds on top.
Place the tart pan on a baking sheet. Bake in the preheated oven for 45 to 55 minutes until the frangipane has risen, is golden brown around the edges, and set in the center.
Once the tart is fully baked, combine the apricot jam and a ½ tablespoon water in a small bowl and mix until combined. Brush over the baked apricots.
Sprinkle additional powdered sugar over the tart if desired, then cut and serve.