Place apricots, butter, water, and sugar in a heavy-bottomed pan over medium-high heat. Bring to a boil, remove from heat, cover, and allow apricots to absorb water (about 30 minutes). Puree in two batches in a food processor, adding lemon juice and, if desired, bourbon to taste. Cover and refrigerate.
Meanwhile, in a large mixing bowl, combine almond paste, butter, and sugar; beat until light and fluffy. Add mascarpone; beat well. Add flour; mix until just combined. In a small bowl, whisk eggs, yolk, salt, and vanilla extract together until frothy. Add to batter; mix until smooth. Cover; refrigerate.
To assemble, bring ingredients to room temperature. Spread the almond-mascarpone cream in bottom of the prepared tart shell (see below) with rubber spatula. Spread apricot filling over cream. Lay second layer of pie dough over the tart; press against edges of pan to trim off excess dough. Refrigerate unbaked pie 30 minutes. Preheat oven to 375 degrees F. Beat egg wash mixture and brush over the top of the chilled crust. Place tart on baking sheet; bake 40 minutes, until tart has puffed up and crust is golden brown.