Heat EVOO in a cast-iron skillet or large, oven-proof skillet over medium-high heat. Add meat and brown well. Add chili pepper, bell peppers, onions, garlic, season with salt and pepper, cumin, coriander and chili powder. Stir and cook to soften peppers and onions, 10 minutes.
Deglaze the pan with the beer. Stir together the vinegar, brown sugar, Worcestershire and tomato sauce in a small bowl. Pour over the turkey and reduce heat to a simmer to thicken and combine flavors.
Preheat broiler.
In a saucepot, bring stock and milk to a boil. Whisk in polenta and cook to thicken, 2-3 minutes. Add honey and stir to combine.
Spread polenta over the turkey in the skillet in an even layer going almost to the edge of the pan. Top polenta with cheese, pop skillet under broiler and brown the top. Serve directly from the skillet.