Combine the coarse semolina flour or cornmeal, fine semolina flour, sugar, and salt in the bowl of a stand mixer fitted with the paddle attachment (or use a hand mixer and a big bowl). Mix on low speed to combine. With the mixer running, stream in the butter, milks, and orange blossom water. Mix just until a smooth dough forms. Shape into 2 equal balls, wrap in plastic wrap, and refrigerate until well chilled, at least an hour or up to overnight.

Put the dates in a bowl and cover with boiling water by 1 inch. Cover the bowl with plastic wrap and let stand for 10 minutes. Drain the dates and puree in a food processor. When cool, add the egg and puree again to combine. 

Preheat the oven to 350°F with a rack in the middle. Divide each dough into 6 equal pieces. Roll each piece into a circle roughly 5 inches in diameter. (If the dough seems stiff, let it stand at room temperature until soft enough to roll without breaking apart.) Press half the dough rounds into the bottom and up the sides of six 4-inch mini tart pans. Spoon the filling evenly into the tartlets and top each with a second circle of dough. Crimp the edges to seal and cut a few slits so steam can escape. Bake until the tartlets are beginning to brown around the edges, about 30 minutes.