Add dough into a 2-inch deep-dish tart pan with a removable bottom or 9-inch pie plate. Gently pressing the dough into the sides. Using a sharp knife, trim the dough evenly with the edge of the pan.
Cover with plastic wrap; chill tart shell until firm, about 20 minutes.
Preheat oven to 375 degrees F.
Line the tart dough with a sheet of parchment paper and fill with pie weights. Transfer to oven and bake until light brown, about 25 minutes. Remove weights and parchment paper and continue baking until golden brown, about 5 minutes. Transfer to a wire rack; let cool completely.
In a 12-inch skillet, add butter and set over medium-high heat.
Add the leeks and cook for 5 minutes or just until it starts to soften.
Add in the swiss chard and cook for a few minutes to just soften slightly. Remove the skillet from the heat and set aside to cool while you make the egg filling.
In a large mixing bowl, whisk together eggs, creme fraiche, and milk until well combined. Add thyme, salt, and pepper; mix until well combined.
Add the cooled leek and Swiss chard mixture to the bottom of the pie crust and spread out evenly. Top with shredded gruyere cheese.
Pour over egg the mixture until the tart shell is full and top with Parmesan cheese.
Bake 20 minutes; reduce temperature to 325 degrees F, and continue baking until filling is slightly firm, rather than liquid and the crust is a deep golden brown, 40 to 50 minutes more.
Transfer the quiche to a wire rack to cool until set, about 20 minutes. Serve warm or at room temperature. To reheat, cover the quiche with aluminum foil and bake in an oven heated to 325 degrees for about 15 minutes.