Over an open flame or in the broiler, char the poblanos until blackened all over, turning occasionally, 10 to 12 minutes. Place in a bowl, cover and let cool. Peel, seed and chop the poblanos.
Preheat a griddle pan or large skillet over medium-high heat; drizzle with a little EVOO. Season the chicken with salt and pepper, add to the pan and cook, turning once, until golden, 12 to 15 minutes. In a microwavable bowl, soften 3 tablespoons butter in the microwave for a few seconds on high. Add half of the cilantro or parsley, the rosemary, the chile powder or paprika and the oregano.
While the chicken cooks, heat a drizzle of EVOO in a saucepan. Add the corn and heat through for a couple of minutes. Add the charred poblano, stir in the milk and chicken stock and bring to a boil. Whisk in the polenta and cook over low heat, stirring, until thickened, 2 to 3 minutes. Stir in the remaining 1 tablespoon butter and the cheese.
Dress the avocado, tomatoes and onion with the remaining cilantro or parsley, the lemon juice and salt.
Slice the hot chicken on the diagonal, then dollop with the spicy butter. Spoon some polenta underneath or alongside the sliced chicken. Serve with the salad.