In a large bowl, stir together the flours and salt with a fork. Scatter the butter over the flour mixture and, using your fingertips or a pastry blender, cut in the butter until the mixture resembles coarse sand with some flattened pieces of butter still visible.

Stir in the ice water, a little at a time, until the dough just sticks together when pressed between your fingertips.

Gather the dough into a ball, wrap in plastic wrap, and flatten into a thick rectangle. Refrigerate for at least 15 minutes. (The dough can be made up to three days ahead and refrigerated; let it rest at room temperature until soft enough to roll out, about 15 minutes.)

Finely chop enough of each of the herbs in any combination preferred to total one and one-fourth cups (75 grams) lightly packed.

In a medium bowl, use a fork to mash together the labneh and feta. Stir in the egg, then stir in the chopped herbs.

Preheat the oven to 425 degrees Fahrenheit (220 degrees Celsius). Have ready two sheet pans. If you like, line them with Gefen Parchment Paper.

Divide the dough in half and rewrap and refrigerate half of it. On a lightly floured work surface, roll out the other half into a rectangle or circle 1/16 to 1/8 inch (two to three millimeters) thick.

Cut out 12 circles each three and a half inches (nine centimeters) in diameter, rerolling any scraps as needed.

Mound one tablespoon of filling in the center of each dough circle. Fold the sides of the dough up over the filling to form a triangle, leaving a nickel-size bit of filling exposed. Pinch the three corners of the triangle very firmly to seal.

Arrange the pastries on a sheet pan, spacing them about one inch (two and a half centimeters) apart. Refrigerate the first batch while you make more with the remaining half of the dough and filling.

Top off the pastries with any leftover filling. Brush the pastries with the egg wash.

Bake the pastries for 12 minutes; the bottoms will be light golden. Reduce heat to 375 degrees Fahrenheit (190 degrees Celsius) and continue to bake until the crust is a rich gold and the filling is puffed and browned in places, 10 to 12 minutes longer.

Using an offset spatula, transfer the pastries to a wire rack and let cool for five to 10 minutes before serving. Refrigerate leftover hamantaschen; they can be reheated in a 350 degrees Fahrenheit (180 degrees Celsius).