Pierce the potatoes a few times with a fork. Microwave until softened but not completely cooked through, 3 to 5 minutes. Let cool slightly, then peel and finely chop; transfer to a medium bowl and set aside.
Bring a large pot of salted water to a boil. Add the spinach and Swiss chard leaves and cook until wilted, about 3 minutes. Drain, then let cool in the colander, tossing occasionally and lightly pressing with a rubber spatula to remove the excess liquid. When cool enough to handle, transfer the greens to a clean kitchen towel and squeeze out as much liquid as possible. Coarsely chop and add to the bowl with the potatoes.
Heat the olive oil in a large skillet over medium-high heat. Add the Swiss chard stems, onion, red pepper flakes, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring, until the vegetables are tender, about 8 minutes. Add the garlic and the spinach-chard mixture; cook, stirring, until well incorporated, 5 minutes. Transfer to a large bowl and let cool to room temperature. Add the cheeses, mint, dill, egg and lemon zest; stir to combine. (You can make the filling 1 day ahead; cover and refrigerate until ready to assemble.)
Preheat the oven to 400 degrees F; line a baking sheet with parchment paper. Lay out 1 sheet of phyllo on a work surface with a long side facing you (keep the remaining sheets covered with a damp towel). Lightly brush with olive oil and lightly sprinkle with breadcrumbs. Fold in half like a book and brush with more olive oil and sprinkle with more breadcrumbs, then fold the top half down. Place 1/2 cup filling in the center and brush the edges with a little water. Bring the top two corners together over the filling and pinch the edges together to seal. Repeat with the bottom two corners; pinch closed. Pinch the two remaining edges closed. Transfer to the prepared baking sheet and brush with olive oil. Repeat to make 8 hand pies.
Transfer the hand pies to the oven and bake until golden brown and crisp, 25 to 30 minutes. Serve warm or at room temperature.
Photograph by Ryan Liebe
Thaw: Place the frozen phyllo in its packaging in the refrigerator overnight (do not thaw in the microwave). Trim: After opening the package, use kitchen shears to trim any edges that are dry or clumped together. Transfer: As you move individual sheets of phyllo, place one hand underneath them to help prevent tearing. Cover: Keep the phyllo covered with a slightly damp kitchen towel while you're working; the sheets can dry out quickly. Store: Stack leftover phyllo on a baking sheet and cover with a damp towel, then wrap tightly with plastic wrap. Store in the refrigerator for up to 3 days; do not refreeze.
Courtesy of Food Network Magazine