Make the crust: Combine the olive oil and water in a measuring cup. Pulse the flour and 1 teaspoon salt in a food processor. With the machine running, add the olive oil mixture and pulse until the dough clumps together, adding up to 1 more tablespoon water if needed. Turn out onto a piece of plastic wrap; press into a disk and wrap. Let sit at room temperature while you make the filling.
Make the filling: Wrap the squash in a kitchen towel and wring out as much liquid as possible; transfer to a large bowl. Repeat with the spinach and add to the squash; stir to break up any clumps. Add the ricotta, fontina, parmesan, half-and-half, scallions, parsley, 2 eggs, the nutmeg, 1 1/2 teaspoons salt and a few grinds of pepper; mix until combined.
Position a rack in the bottom of the oven; preheat to 375 degrees F. Brush a quarter sheet pan or 9-by-13-inch straight-sided baking pan with olive oil. Cut off one-quarter of the dough; set aside. Roll out the remaining dough into an 11-by-15-inch rectangle on a floured surface. Trim the edges with a fluted cutter or a knife and ease into the pan. Spread the filling over the dough.
Roll out the reserved dough into a 6-by-12-inch rectangle on a floured surface. Cut lengthwise into 10 strips with the fluted cutter; arrange in a lattice pattern over the filling, trimming as needed. Fold in the overhanging edges. Beat the remaining egg with a pinch of salt and brush on the crust. Bake until the crust is golden and the filling is set, about 50 minutes. Let cool on a rack 30 minutes before cutting.