Spiced poached apricots top this beautiful tart, but they would be equally delightful spooned over a bowl of vanilla ice cream. Martha made this recipe on Martha Bakes episode 605.
Make the poached apricots: Combine wine, 3 cups water, sugar, vanilla pod and seeds, and cinnamon stick in a large straight-sided skillet. Bring to a simmer over medium heat, stirring until sugar dissolves. Add apricots, cut-side down. Cover surface with a parchment round, and cook, simmering, until apricots are just tender, 3 to 5 minutes. Using a slotted spoon, transfer poached apricots to a small rimmed baking sheet or plate.
Bring poaching liquid to a boil and cook until reduced to about 3/4 cup, about 20 minutes.
Meanwhile, preheat oven to 400 degrees with rack in lower third of oven. Make the frangipane: Combine hazelnuts and sugar in bowl of food processor and process until finely ground. Add butter, flour, egg, liqueur, salt, and vanilla extract; process until frangipane is smooth.
Prepare the tart shell: Unfold puff pastry on parchment paper-lined baking sheet. Using a paring knife, lightly score a border about 1 1/2-inches in from perimeter of pastry.
Using tines of a fork, pierce puff pastry all over within border. Spread frangipane in an even layer within border. Arrange poached apricots on top of frangipane, cut-side down; brush lightly with poaching liquid. Combine egg and cream, then brush lightly onto puff pastry border.
Bake until tart is puffed and golden brown, 35 to 40 minutes. Transfer to a wire rack and brush apricots lightly with more poaching liquid. Let cool completely.