Set oven rack two levels below broiler element and heat oven to broil. Line a baking dish with foil and set Poblano pepper on foil. Transfer to oven and broil pepper, rotating frequently, until skin has blistered and charred, about 8 - 10 minutes.
Transfer pepper to an airtight bag, seal bag and allow to rest 5 minutes, or until cool enough to handle. Remove from bag and peel pepper, cut off top, make one slice down length of pepper. Remove and discard seeds and ribs. Pat inside of pepper dry with a paper towel, set aside.
Heat 2 tsp oil in an 8-inch non-stick skillet slightly over medium heat. Whisk egg vigorously in a small bowl until frothy, 1 minute. Once oil is hot, carefully pour egg into pan.
Cook egg until golden, about 10 seconds, then using a spatula, fold egg into a half (as if you were making an omelet). Continue to cook just until nearly cooked through, about 10 seconds longer per side then transfer to paper towels to drain, set aside.
To assemble sandwich, brush 1/2 tbsp butter on outsides of bread. Layer egg on bread, followed by roasted Poblano pepper, grated Wisconsin Monterey Jack cheese and sprinkle top with half of the pico de gallo (reserve remaining pico de gallo for another use).
Using paper towels, wipe oil from skillet. Heat skillet over medium-low heat. Carefully transfer assembled sandwich to skillet.
Cook until bottom is golden about 4 - 6 minutes, then rotate sandwich to opposite side, cover skillet with lid and cook opposite side until golden brown and cheese has melted through, about 4 - 6 minutes. Serve immediately.
FOR THE PICO DE GALLO: Combine diced tomato, onion, garlic, cilantro and lime juice in a small mixing bowl. Season with salt and pepper to taste.
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