Pour milk into small saucepan. Scrape in seeds from vanilla bean; add bean. Bring to simmer. Remove from heat.
Whisk yolks, sugar and cornstarch in bowl to blend. Gradually whisk milk mixture into yolk mixture. Return to pan.
Whisk over medium heat until custard thickens, about two minutes. Transfer to bowl to cool.
Discard vanilla bean.
Preheat oven to 350°F.
Sift flour onto work surface. Make a well in center and add lightly softened butter. Add the remaining ingredients and knead into a ball. If the mixture is slightly sticky, add a bit more flour. Wrap the dough ball in plastic and let stand in the refrigerator for one hour.
Remove the dough from the refrigerator and let it sit at room temperature for one hour.
Roll out pastry on floured surface to 14-inch round. Transfer to 11-inch diameter tart pan with removable bottom. Press crust into pan. Trim edges to ½ inch overhang; fold in dough and press, forming double-thick sides. Cover dough with parchment paper and fill with raw rice to help keep the shape of the tart even. Bake until light golden brown, about 20 minutes, then let cool. Maintain oven temperature.
Finely grind almonds and powdered sugar in processor. Add cooled custard; blend together. Blend in butter, whole egg, almond extract and salt. Pour into crust; smooth top.
Arrange apricot halves, round side up, atop filling.
Bake tart until filling is set and golden brown, about 40 minutes. Remove from oven. Brush top of tart with honey.
Return to oven for five minutes until honey forms a glaze. Cool completely in pan.