Make the dough: In a large bowl, whisk the kefir, milk, yeast, and honey. Set aside until bubbles appear on the surface, about 10 minutes. Use a wooden spoon to slowly stir in half of the flour until you have a soft, very wet dough. Cover the bowl with plastic wrap and set aside in a warm place to rise for about 40 minutes.
Meanwhile, make the browned butter glaze: Set a small, heatproof bowl by the stove. In a small saucepan over medium-low heat, melt 3 tablespoons of the butter. Cook until foamy, then continue cooking, swirling the pan occasionally, until deep golden brown and nutty smelling, about 3 minutes more. Transfer the butter to the bowl, using a spoon to scrape the browned milk solids from the bottom of the pot. Set aside.
Make the filling: In a large skillet set over low heat, melt the remaining 2 tablespoons of butter and cook until foamy. When the foam begins to subside, add the garlic and cook until fragrant but not yet browned, 2-3 minutes. Add the greens and cook until the stalks begin to soften but still retain texture, 4-6 minutes. Stir in the lemon zest, then transfer the mixture to large bowl, and set aside to cool completely.
Preheat the oven to 425°. Meanwhile, line 2 baking sheets with parchment paper.
Add the Ogleshield or raclette, the feta, spring onions, and dill to the cooled beet mixture; season with flaky sea salt and black pepper and stir well to combine. Divide the filling evenly into 3 portions, about 9 ounces or 3½ cups each. Shape each into a ball, and set aside.
Lightly flour your hands and a clean work surface. One at a time, transfer the doughs to the surface, then knead the fine sea salt and just enough of the remaining flour into the risen dough until it stops sticking to your hands but still feels still soft and pillowy. Divide the dough into 3 equal pieces, about 6 ounces each. Flatten each piece with your hands and roll each out into an 8-inch round. Place one ball of filling in the center of each round. Bring the edges of the dough up over the filling, pinching and pleating the ends together at the top to secure them like dumplings. Sprinkle each pouch with flour, then flip them so that the knotted sides are on the bottom. Use your hands to flatten the pouches gently, pressing the filling inside all the way to the edges and stretching the pies back to 8-inch rounds.
Transfer the pies to the lined baking sheets and cut a small slit in the center of each to let steam escape. Transfer the baking sheets to the oven and bake until the dough is deep golden all over and the bottoms are dry and crispy, 20-25 minutes. Remove from the oven and brush immediately with brown butter. Let the pies cool slightly, then cut into wedges and serve immediately.