Preheat oven to 375 degrees F.
Roast the poblano and jalepeno chiles directly in the flame of a gas burner, turning until charred on all sides. (Alternatively, if cooking with an electric stove, broil until charred.) Put chiles in a bowl, cover and steam until soft and cool, about 20 minutes. Peel, seed, and chop.
Spread the tomatillos on a foil-lined pan, season with salt, pepper and drizzle with olive oil. Bake in the oven until soft and slightly charred, 30 minutes. Meanwhile, cut tortillas into wedges and lay out on a parchment-lined baking sheet. Spray both sides with olive oil spray and bake until crisp and golden, turning half way in between, 8 minutes per side.
Saute onions and garlic in 3 teaspoons extra-virgin olive oil until soft and starting to brown, 8 minutes. Add peppers, tomatoes, cumin, paprika, sugar and water and cook until tomatoes begin to burst and flavors come together, 5 minutes.
Divide sauce between 4 small dishes. Poach eggs and lay 1 egg on each plate over sauce. Garnish with a couple of baked tortillas, crumbled queso fresco, a pinch of paprika and chopped cilantro.
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