In a food processor, combine flour, sugar, salt and baking powder in bowl fitted with metal blade. Pulse 3 times at 1-second intervals to mix. Add butter to work bowl and pulse about 15 times until mixture is fine and powdery and resembles coarse ground cornmeal and no large pieces remain. Add the eggs and pulse ten times or so, until the dough forms a ball. Scatter a teaspoon of flour on the work surface and scrape the dough out onto it. Press and knead the dough quickly 3 or 4 times, until it is smooth and uniform. Press the dough into 2 equal disks. Sandwich the disks of dough between two pieces of plastic wrap and press into a 6-inch circle. Refrigerate the dough until firm, or until you are ready to use it, at least 1 hour.
To make the filling, pit the cherries over a bowl. Slash the side of each one with a stainless steel paring knife and squeeze gently to extract the pits. Put the cherries in the bowl as they are pitted. When all the cherries have been pitted drain the juices from the bowl into a non-reactive saucepan and add 1 cup of the cherries and the sugar. Bring to a simmer over low heat, stirring occasionally, until the sugar is melted and the mixture is very liquid--about 5 minutes. Combine the cornstarch and water in a small bowl and whisk the cherry and sugar mixture into it. Return to the pan and cook, stirring constantly, over low heat, until it comes to a boil thickens and becomes clear. If it does not become clear, continue to cook over low heat an additional few minutes until it does. Pour into a large bowl and stir in the remaining filling ingredients, except the cherries then add the remaining cherries. Set racks at the upper and lower thirds of the oven and preheat to 400 degrees. Roll out the bottom crust and arrange in pan. Pour the cooled filling into the bottom crust. Prepare a diagonal lattice top crust. Flute the edge of the pie and carefully brush it with egg wash. If you wish, sprinkle the top the pie with sugar. Place the pie in the oven an and lower the temperature to 375 degrees. Bake for about 40 minutes, until the crust is baked through and a deep golden brown and the filling is gently bubbling. If the top crust has not colored sufficiently after 30 minutes, move the pie to the upper rack of the oven for the last 10 minutes. Cool the pie on a rack. Serve wedges of pie alone or with ice cream. Keep the pie at room temperature on the day it is baked. For longer storage, refrigerate the pie well wrapped in plastic. To reheat remove the plastic and bake the pie at 350 degrees for about 15 minutes before serving.