Mix cilantro, mustard, mustard seeds and garlic in a small bowl.
Remove stems and scrape the black gills from the undersides of the mushrooms; season with salt and pepper. Brush oil evenly over a 10-inch cast-iron or other ovenproof skillet. Heat skillet over medium-high heat. Add mushrooms, rounded side down, and sear 2 minutes. Remove from the heat, turn over and spread mustard mixture over browned side. Transfer the pan to oven and roast until tender, about 15 minutes.
Transfer the mushrooms to a cutting board and carve into slices. Spoon some New Mexico Chile Sauce onto 2 plates and top with the mushroom slices. Serve immediately.