For the topping:
2 cups all-purpose flour
½ teaspoon salt
13 tablespoons (1 stick plus 5 tablespoons) unsalted butter
6 tablespoons Greek yogurt
1 tablespoon white wine vinegar
¼ cup ice water
1 egg beaten with 1 tablespoon water, for egg wash
For the filling:
2 tablespoons olive oil
4 ounces ¼-inch-diced pancetta
1 large onion, finely chopped
2 carrots, finely chopped
2 celery stalks, finely chopped
Pinch of red pepper flakes
Salt and freshly ground black pepper
2 garlic cloves, minced
4 cups (8-10 ounces) thinly sliced Swiss chard leaves
3½ tablespoons unsalted butter
3½ tablespoons all-purpose flour
2 cups low-sodium chicken broth
1¼ cups low-sodium beef broth
2 cups cooked white beans, drained
To make the pastry topping, combine the flour and salt in a large bowl. Add the butter and use your fingers or a pastry blender to work the butter into the flour until it resembles uncooked couscous.
In a small dish, whisk together the Greek yogurt, vinegar and water. Pour the liquid mixture into the flour mixture and use a spatula to mix together until a rough dough forms. Knead the dough a couple times until a ball forms. Pat the dough into a flattish ball, wrap in plastic wrap and chill in the refrigerator for at least 1 hour and up to 2 days.
To make the filling, heat 1 tablespoon of oil in a large, wide saucepan over medium-high heat. Add the pancetta and cook, stirring frequently, until crisp on all sides, 8-10 minutes. Use a slotted spoon to remove it to a paper towel, then transfer to a medium bowl. Leave the heat on and the drippings in the pan.
Add the remaining tablespoon of oil to the pan, if needed, and heat until shimmering. Add the onions, carrot, celery, red pepper flakes and a few pinches of salt. Cook over medium heat until the vegetables are softened, 7-8 minutes. Add the garlic and continue cooking another minute. Add the greens and cook for 2-3 minutes, or until they’re wilted. Transfer all the vegetables to the bowl with the pancetta and set aside.
Melt the butter in the saucepan over medium-low heat. Whisk in the flour, then continue cooking for 2 minutes, whisking constantly, until it begins to darken. Very slowly whisk in the broths, whisking constantly. Once you’ve added about a third of the broth, you can add the rest more quickly. Use the whisk to scrape up any browned bits from the bottom of the pan.
Stirring constantly, bring the broth mixture to a boil. Reduce to a simmer and cook for 10-12 minutes, until the sauce is thickened and gravy-like. Taste and add salt and pepper as needed. Stir in the white beans and vegetable mixture.
Heat the oven to 375º. Divide the filling between four oven-safe 2-cup bowls (you’ll have about 1½ cups of filling in each), then place them on a baking sheet. Divide the dough into four pieces. Roll each into a round on a lightly floured surface, making sure to roll about 1 inch wider than your bowls. Whisk the egg wash and brush it lightly around the rim of each bowl (to help hold the crust in place). Drape the pastry over each bowl, pressing gently to adhere. Brush the dough with egg wash, then cut vents to allow steam to escape.
Bake until the crust is lightly bronzed and the filling is bubbling, 30-35 minutes.