In a saucepan large enough to hold the milk, combine the milk and a pinch of nutmeg and bring to a simmer over very low heat. Simmer gently, stirring occasionally, for 1 minute, then remove from the heat.
In a saucepan of the same size, melt the butter over low heat. Stir in the flour, raise the heat to medium-low, and cook, stirring constantly with a wooden spoon, until the flour smells fragrant but is not yet darkening, about 3 minutes. Remove the pan from the heat, let the butter mixture cool slightly, and then slowly whisk the warmed milk into the butter-flour mixture until it is fully incorporated.
Return the pan to low heat and bring the mixture to a very gentle simmer, whisking continuously to prevent any lumps from forming. Taking care the mixture does not boil, cook the mixture, whisking occasionally, until it is the consistency of a thick cream-based soup, about 10 minutes. Season with salt and pepper.
For the Flaky Tart Pastry:
In a large bowl, whisk together the flour, sugar, and salt. Scatter the butter pieces over the top, then, using your fingertips or a pastry blender, mix briefly until evenly combined. Add the shortening and continue working the mixture with your fingers or a pastry blender until it feels powdery, dry, and soft, and some pea-size pieces of butter and shortening are visible. Drizzle in the water and, using a rubber spatula, stir and toss the mixture until it is dry and coarse and begins to form small balls that stick together slightly. If the dough does not stick together, add another 1 or 2 tablespoons water.
Working quickly, gently gather the dough together into a rough mass. Transfer the dough to a lightly floured work surface, press together gently, and then divide in half. With your fingers, press each half into a round, smooth disk about 6 inches in diameter. Wrap each disk very tightly in plastic wrap. Refrigerate for at least 1 hour before using, though overnight is best. It will keep refrigerated for up to a week.
For the Spinach Tart:
Have ready the pastry dough and béchamel sauce. If using fresh spinach, wash it thoroughly, then transfer it, still wet, to a large pot. Place over medium heat, cover, and cook, stirring occasionally, until it has wilted but is still bright green, about 4 minutes. Pour into a colander. When it’s cool enough to handle, squeeze out as much of the liquid as possible, then chop it coarsely. If using frozen spinach, squeeze out as much of the liquid as possible and chop coarsely.
In a skillet, cook the bacon over medium heat, stirring occasionally, until just golden, about 4 minutes. Transfer it to a large bowl. Add the spinach and béchamel sauce to the bowl and mix well. Add pepper to taste and stir to combine. Taste for seasoning, adding a pinch or two of salt if necessary.
Fifteen minutes before baking, remove the two dough disks from the refrigerator, unwrap, and dust each lightly with flour. Preheat the oven to 375°F. Have ready a 91⁄2-inch pie plate. On a lightly floured work surface, roll out one disk, working from the center outward and rotating it clockwise a quarter turn after every few passes, until you have a circle about 131⁄2 inches in diameter and 1⁄8 to 1⁄4 inch thick. If the dough sticks to the rolling pin, dust the dough with a tiny bit more flour. To lift the pastry easily into the pie plate, place the plate next to it. Set the rolling pin in the center of the round, fold half of the dough over it, and then lift the rolling pin to place the dough onto the plate. Gently press the dough into the bottom and up the sides of the plate (there will be overhanging pastry). Prick the bottom about twenty times with the tines of a fork. Pour the spinach mixture into the pastry-lined pie plate. Roll out the second disk using the same method. Lift the dough round and carefully slide it over the filling. Using scissors, trim the overhang to 1 inch. Fold the 1-inch overhang under itself to create a high lip and crimp the edge with your fingers or with the tines of a fork. Use the scissors to clip a few rows of small vents in the top crust. Brush the top crust and the edges with the egg yolks. Bake until the crust is evenly golden brown, about 1 hour 10 minutes. Let cool slightly on a wire rack and serve hot, or let cool and serve at room temperature.