Heat oil in medium cast-iron skillet over low heat. Add poblano chili and garlic and saute until chili begins to soften, about 8 minutes. Increase heat to medium. Add mushrooms; saute until tender, about 6 minutes. Season with salt and pepper. (Can be made 6 hours ahead. Cover; chill. Re-warm over medium heat before continuing.)

Prepare barbecue (medium-low heat). Transfer cast-iron skillet to barbecue rack. Add cheese to hot mushroom mixture. Stir until cheese melts and mixture begins to bubble, about 4 minutes. Sprinkle green onions and jalapeno chili over. Serve immediately with corn chips.

Serves 4.