1 bunch white Swiss chard (about 12 ounces), washed and dried
1/2 bunch scallions (3 to 4)
2 tablespoons olive oil
Freshly ground black pepper
8 tablespoons unsalted butter, melted and still hot
2 large eggs, lightly beaten
1 cup crumbled feta cheese (about 4 1/2 ounces)
2 tablespoons coarsely chopped fresh dill leaves
10 (14x18-inch) phyllo sheets (about 8 ounces), thawed if frozen
Cut the stems from the chard. Cut the stems crosswise into 1/4-inch-thick pieces and set aside. Stack the leaves and cut into 1-inch pieces; keep separate from the stems. Thinly slice the scallions.
Heat the oil in a large frying pan over medium heat until shimmering. Add the scallions and chard stems, season with salt and pepper, and cook, stirring occasionally, until softened, about 8 minutes. Add the chard leaves, season with salt, and cook, stirring occasionally, until completely wilted, about 6 minutes.
Transfer the mixture to a fine-mesh strainer set over a bowl. Place in the refrigerator and stir occasionally until cooled to room temperature, about 20 minutes. Meanwhile, arrange a rack in the middle of the oven and heat to 400°F. Brush the sides and tube of a 10-cup Bundt pan with melted butter; set aside.
When the chard mixture is cooled, pick it up by the handful, squeeze out the excess moisture, and place on a cutting board. Finely chop the mixture, then transfer it to a large bowl. Add the eggs, feta, and dill, and mix to combine.
Lay one sheet of phyllo on a work surface, positioning a long end to face you. (Don't worry if the phyllo rips — just patch it back together.) Keep the remaining phyllo covered with plastic wrap, wax paper, or a damp kitchen towel. Brush the phyllo with a thin layer of melted butter. Repeat with the layers of phyllo, brushing each layer, until all the phyllo is used up, making sure to brush the top layer of phyllo with butter. (Rewarm the butter as needed to be able to brush a thin layer.) Season the surface of the phyllo with salt and pepper.
Spread the chard mixture thinly on the phyllo, leaving a one-inch border. Starting from the end closest to you, roll the phyllo tightly up like a jelly roll. Brush the entire outside of the roll with butter. Pick up the roll and place it seam-side up in the Bundt pan, winding it around the tube and making the ends meet.
Bake until flaky and golden-brown, about 40 minutes. Immediately flip it out onto a wire cooling rack set over a baking sheet. Let cool 10 minutes. Transfer to a cutting board and cut into 12 slices with a serrated knife.