To make the frangipane, place the almonds and the sugar in a food processor and grind until sandy. Add the butter and continue mixing then add the egg, vanilla, and the flour and mix until smooth.
To make the tart, on a floured work surface pass your rolling pin over the pastry just to flatten any ridges.
Place it on a parchment paper lined sheet pan and cut out a 9-inch disk. Spread the almond frangipane in the center of the tart leaving a 1-inch border. Firmly place the apricot halves into the frangipane spacing them evenly around the tart. Dot the spaces between the apricots with the whole almonds.
Bake until golden brown on the top and puffy, about 30 to 40 minutes. Sprinkle with powdered sugar and serve.