First, make the crust: In the bowl of a stand mixer fitted with the paddle attachment, add the flour, sugar, and salt. Mix briefly on low speed. Add the butter cubes and continue mixing on low until they have broken down into pea-size pieces, 4–5 minutes. With the mixer still running, drizzle in 3 tablespoons of ice-cold water water and continue mixing just until a dough begins to form, 15–30 seconds.
Transfer the dough to a large piece of plastic wrap. Using your hands and the plastic wrap, press it together into a cohesive mass, then flatten the dough into a 1-inch thick disk and wrap it tightly. Refrigerate for at least 1 hour or up to 3 days before using.
When ready to bake, in a large skillet set over medium-high heat, add the pancetta and cook, stirring frequently, until crispy and slightly browned, 5–7 minutes. Transfer the pancetta to a small, heat-resistant bowl, leaving behind any rendered fat in the skillet. Add the olive oil to the skillet and swirl for a few seconds to heat thoroughly, then add the shallots and ¼ teaspoon of salt. Stir well, scraping the bottom of the skillet to deglaze any brown bits left by the pancetta, then lower the heat to medium low and cook, stirring frequently, until the shallots are translucent and just beginning to brown 12–14 minutes. Add the kale, mustard greens, garlic, and the remaining ½ teaspoon of salt and continue cooking, tossing occasionally, until the greens are wilted and tender, 15–20 minutes. Return half of the cooked pancetta to the skillet and stir well to combine. Then transfer the mixture to a large bowl; set it aside to cool at room temperature.
Preheat the oven to 400°F. In a medium bowl, add the crème fraiche, gruyère, and mustard, and stir well to combine. Set aside.
Retrieve the dough from the fridge and unwrap. Cut a piece of parchment paper to fit a large baking sheet, and place it on a clean work surface. Lightly dust it with flour. Place the dough on top and roll it out to an even 14-inch circle, about ⅛ inch thick. Transfer the dough to the baking sheet.
Transfer the dough to the baking sheet. Using a spatula or the back of a spoon, spread the crème fraiche mixture evenly over the dough, leaving a 1–2 inch border around the edges. Transfer the greens mixture on top, distributing it evenly, then sprinkle with the remaining pancetta. Fold and crimp the edges of the dough all the way around the galette to make a 1-inch lip. Brush the edges of the crust with the prepared egg wash.
Bake until the edges are golden brown and the filling is hot and bubbly, 40–45 minutes. Cool slightly, then use a wide spatula to slide the whole gallette onto a serving platter. Slice into wedges and serve warm or at room temperature