In a bowl, combine all-purpose flour, extra-virgin olive oil, cold water, and coarse salt. Stir with a fork to combine, then turn out onto a work surface and knead 1 minute. Cover dough with plastic wrap and let rest at room temperature, 30 minutes.
In a large pot, heat oil over medium-high. Add onion and garlic; cook until onion begins to soften, about 2 minutes. Add chard stems and red-pepper flakes; cook until stems begin to soften, about 2 minutes.
Pack chard leaves into pot; season with salt and pepper. Reduce heat to medium, cover, and cook until chard leaves wilt, about 4 minutes. Uncover and cook, stirring occasionally, until chard is soft, about 4 minutes. Drain, pressing out as much liquid as possible. Place chard mixture in a large bowl and toss with Parmesan, flour, lemon zest and juice. Season with salt and pepper.
Roll two-thirds the dough to a 12 1/2-inch round; fit into an 8-inch round cake pan (2 inches deep). Fill bottom crust with chard mixture. Roll remaining dough to a 9 1/2-inch round; place over filling. Pinch edges of dough together and tuck in to seal; cut several vents into center of pie. Combine yolk with 1 teaspoon water and brush over dough, avoiding edge of pan. Freeze pie (see below).
To serve, preheat oven to 400, with rack in lowest position. Bake frozen pie until crust is deep golden brown, about 1 1/2 hours. Serve warm or at room temperature.