For the dough: In a medium bowl, whisk together the eggs and water; set aside. In the bowl of a food processor, combine the flour and salt and pulse a couple of times. Add the chilled butter and pulse about 10 times until pea-size pieces remain. Add the egg mixture and pulse 15 to 20 times until a dough ball forms. Place the dough ball on a floured surface and knead until smooth and elastic, about 1 minute. Divide into 2 balls, wrap each ball with plastic wrap and rest in the fridge for at least 1 hour.
For the filling: While the dough is resting, whisk together the ricotta cheese, salt, some pepper and 6 of the eggs in a medium bowl and set aside. In a 10-inch skillet over medium heat, add the oil and brown the sausage, breaking up the pieces while it's cooking, 5 to 8 minutes. Drain the sausage on a paper towel-lined plate, leaving behind any fat. Add the asparagus and cook until beginning to soften, 4 to 5 minutes. Set aside.
Preheat the oven to 375 degrees F. Grease a 9-inch cake pan with butter.
On a well-floured counter, roll out each dough ball into a thin 14-inch circle. Cover one circle with plastic wrap until ready to use. Loosely roll the other dough circle around a rolling pin and unroll over the prepared cake pan, letting the excess hang over the side. Press the dough gently into the sides of the pan so there is no gap between the pan and the dough. Shingle the salami over the bottom of the dough, creating an even layer. Then, add the asparagus in an even layer on top of the salami. Next, add half of the egg mixture and spread it out evenly, then top with the capicola in an even layer. Layer in the sausage and top with the remaining egg mixture, then finally the provolone cheese.
Whisk the remaining egg with 1 tablespoon water and brush the outside rim of the dough with the egg wash. Add the remaining dough circle to the top of the pie and cut off the excess dough. Press both circles together to create a seal. Brush the remaining egg wash over the entire top and slice a couple slits in the top of the pie. Bake until golden brown, 45 to 55 minutes. Let stand 10 minutes before slicing.