How to Make It
In a large saucepan of boiling water, cook the potatoes until fork-tender, about 20 minutes. Drain, cool slightly and peel. Transfer to a large bowl and mash roughly.
Using a small sharp knife, slit the chiles lengthwise, leaving the stems intact. Carefully remove the seeds and veins. Place the chiles in a bowl, cover with hot water and let soak until just beginning to soften, about 20 minutes (depending on how dry they were in the first place). Drain.
Add the cheese to the potatoes, season with salt and mash together well. Stuff the chiles fully with the filling, but leave enough room so that the seams almost close.
Heat the oil in a large nonreactive skillet. Gently fry the chiles in batches, rolling them over from time to time so that they cook evenly without browning too much, about 5 minutes. Transfer to paper towels to drain. Reserve the oil in the skillet.
In a large nonreactive saucepan, cover the tomatillos with water and simmer until soft, about 10 minutes. Drain and transfer to a blender. Add the onion and garlic and blend until almost smooth (but still textured).
Preheat the oven to 350°. Heat the reserved oil in the skillet. Add the brown sugar and fry for a few seconds. Add the tomatillo sauce, season with salt and cook over high heat until reduced, about 5 minutes. Stir in the chicken stock.
In a baking dish large enough to hold the chiles in one layer, arrange the chiles side by side. Pour the tomatillo sauce over the chiles and bake until heated through, about 15 minutes. Serve warm.