1In a medium bowl, combine the 1 cup of flour, chili powder and salt. Use a pastry cutter to add the butter, working it until the butter is in large pea-sized pieces. In a small bowl, whisk the egg and water. Add the egg mixture to the flour mixture, and use your hands to start kneading them together. Add the remaining 1/3 cup of flour, a little at a time, transferring the mixture to a lightly floured work surface if you like, kneading until you have a smooth, supple dough (you might not need all the flour). Shape the dough into a 3/4-inch thick disk, cover with plastic wrap and set aside in the refrigerator for at least 1 hour. (Alternately, you can use an electric mixer or food processor to make the dough.)
2Meanwhile, in a medium skillet over medium-low heat, warm the oil. Add the ham and tomatoes and cook, stirring occasionally, until the tomatoes become thick and sauce-like, about 10 minutes. Remove from the heat and set aside.
3Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper or a silicone baking mat and set aside.
4On a lightly floured work surface, roll the dough out to a 10-inch circle. Transfer the dough to the prepared baking sheet and top with the ham mixture, leaving a 1- to 1 1/2-inch border around the edges. Top with the cheese and spinach. Fold the dough over the edge of the fillings, pinching it firmly together every inch or two. Brush the edge of the dough with the egg white (you won’t need it all) and bake until crust is golden, 30 to 35 minutes.
5Cool 5 to 10 minutes before slicing and serving.