Set a rack in the lower third of the oven and preheat to 350 degrees.
For the dough, combine 3 cups flour, 1/2 cup sugar, baking powder, and 1/2 teaspoon salt in the bowl of a food processor and pulse to mix. Cut butter into 12 pieces and add. Pulse repeatedly until butter is mixed in finely. Add 3 eggs and continue to pulse until dough forms a ball. Wrap and chill dough while preparing filling.
Rinse, stem, halve and pit the apricots. Combine the 3/4 cup sugar, 6 tablespoons flour and pinch of salt in a mixing bowl and whisk to mix. Whisk in the 6 eggs, 2 at a time, then whisk in the cream and vanilla. Cut off 2/3 of the dough. Roll it on a floured surface and use it to line a 10-inch round prepared pan. Trim dough even with top rim of pan. Arrange the apricot halves, skin side down, slightly over-lapping, and in concentric circles, in the dough-lined pan. Pour the cream and egg mixture over the apricots.
For the top crust, roll remaining dough to a 8 by 10-inch rectangle and cut into ten 3/4-inch by 10-inch strips. Arrange 5 strips on the filling, then arrange another 5 strips diagonally to the first ones to form a lattice. Trim ends of dough even with rim of pan.
Bake the tart for about 1 hour, until the pastry is baked through and the filling is set. Plunge the point of a thin knife into the center of the tart, it should emerge fairly clean. Cool the tart on a rack and serve it at room temperature.