Make the crust: Put the flour, sugar and fine salt in a food processor and pulse to combine. Add the butter and pulse until the mixture looks like coarse meal. Add 2 tablespoons ice water and pulse until the dough just comes together, adding up to 2 more tablespoons ice water if needed. Transfer to a sheet of plastic wrap and pat into a disk; wrap and refrigerate until firm, about 1 hour.
Coat a 9-inch springform pan with cooking spray. Roll out the dough into a 12-inch round on a floured surface. Ease into the prepared pan and press into the bottom and up the side; trim to make a 2-inch-high crust. Prick the bottom a few times with a fork; refrigerate 30 minutes. Preheat the oven to 350 degrees F.
Place the dough-lined pan on a baking sheet. Line the dough with foil and fill with pie weights or dried beans. Bake until the edges are just lightly golden, about 20 minutes. Remove the foil and weights; continue baking until the crust is lightly golden all over, 15 to 20 more minutes. Transfer to a rack to cool completely. (The crust can be made a day ahead; cover and store at room temperature.)
Make the filling: Thinly slice the Swiss chard leaves and cut the stems into 1/4-inch slices. Heat the olive oil in a large skillet over medium-high heat. Add the onion and chard stems, season with kosher salt and pepper and cook, stirring occasionally, until the onion is soft and just beginning to brown, about 10 minutes. Add the dill and lemon zest and cook, stirring, 30 seconds. Add the chard leaves and cook, stirring, until wilted, about 4 minutes. Remove from the heat and stir in the parsley, 3/4 teaspoon kosher salt, and pepper to taste. Let the filling cool, then squeeze out the excess moisture.
Transfer the filling to a food processor; pulse until coarsely chopped. Transfer to a bowl and stir in the shredded cheddar, half-and-half, parmesan, egg and nutmeg. Pour into the crust and bake until set, 45 to 50 minutes. Top immediately with shaved cheddar and let melt. Serve warm or at room temperature.