1. Make potatoes: Preheat oven to 475°. Purée chipotles and sauce in a blender. Spoon 2 tbsp. into a bowl; save the rest for other uses. Stir in oil, salt, and pepper, then potatoes.
2. Spread potatoes on a rimmed baking sheet lined with parchment paper, leaving a corner empty; put poblano in corner. Bake, turning chile and potatoes occasionally, until chile is blackened and potatoes are well browned, 20 to 25 minutes. Let cool. Peel, stem, seed, and coarsely chop chile. In a plastic container, combine potatoes, chile, and onions; chill until used, up to 2 days.
3. Whisk eggs and milk in a bowl to blend with 1/4 tsp. each salt and pepper; set aside. Heat a large cast-iron skillet over medium-high heat. Melt butter, then add potato mixture and stir occasionally with a flexible spatula until hot, 2 to 3 minutes.
4. Add egg mixture, reduce heat to medium, and cook, scrambling gently, until set, 2 to 4 minutes; add cheese and cilantro during last minute. Serve with salsa, crème fraîche, and tortillas, plus more salt and pepper to taste.
*Double-wrap tortillas in foil and warm over low heat, turning often.
Note: Nutritional analysis is per serving.