Heat broiler to high with the rack in the upper third of oven. Char peppers and tomatillos, turning peppers occasionally to char evenly all over. Place in a bowl and cover with plastic wrap to cool. Peel and seed peppers.
Place charred peppers, tomatillos, 2 cups stock, cilantro, salt, pepper, honey and cumin in food processor and process until smooth.
Meanwhile, heat a large, cast-iron or other heavy pan over medium-high heat with oil, 2 turns of the pan. When oil smokes, brown and crumble meat then add onions and garlic. Season with salt and pepper, and cook to soften onions, 5 minutes. Deglaze with beer and stir in salsa. Bring to a bubble and reduce heat to simmer. Stir in sour or heavy cream.
In a saucepot, heat remaining 2 cups stock and milk. Whisk in polenta or cornmeal and let thicken 2-3 minutes until very thick but still pourable. Season with salt and pepper, and stir in butter. Spread the corn topping over the turkey filling, place under the broiler and char to set polenta. Top with cheese then melt cheese under broiler. Serve directly from skillet, topped with red onion rings.