For the crust: Combine the flour, almonds, sugar and salt in a food processor and blend until the nuts are finely ground. Add the butter and pulse until the mixture resembles a coarse meal. Pour in the vodka and 1 tablespoon water and pulse until the dough just comes together in a soft dough. Turn the dough out onto a piece of plastic wrap, press it into a disc and refrigerate until slightly firm, about 20 minutes.
Turn the dough out into a 9-inch tart pan with a removable bottom. Top with a piece of plastic wrap and press the dough out evenly through the plastic wrap on the bottom and up the sides of the pan. Freeze until firm, about 30 minutes.
Preheat the oven to 375 degrees F. Pierce the dough lightly with a fork, and then line the crust with parchment or foil and fill with pie weights, beans or rice. Bake until the crust sets, about 20 minutes. Remove the parchment and beans and then return to the oven until the crust turns a rich golden brown, about 15 minutes longer. Let cool.
For the apricot and chocolate filling: Combine the apricots, brandy and 1/4 cup water in a microwave-safe bowl. Cover and microwave for 2 minutes, and then set aside to plump.
Put the chocolates in a medium bowl. Heat the half-and-half in a small saucepan over medium heat. Whisk together the eggs and sugar in a separate medium bowl, and then gradually whisk in the heated cream. Pour back into the pan and cook, stirring constantly with a heatproof spatula, over medium-low heat until thick, about 1 minute. Pour the mixture over the chocolate, let set for 5 minutes, and then whisk in the butter until very smooth.
Blend the apricots and their liquid with the vanilla in a mini food processor until very smooth. Spread 3/4 cup of the mixture over the bottom of the crust. Top with the chocolate mixture. Cover loosely and refrigerate until set, about 3 hours or up to overnight.
Meanwhile, whip the cream until it barely holds soft peaks. Whisk in the remaining apricot mixture to make a smooth thick cream. Cover and refrigerate until ready to use. To serve, pipe or spoon small dollops of the cream around the edge of the crust.