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1. Chicken: Whisk 3 tbsp oil, lime juice, garlic, paprika, sugar, salt, cumin, pepper, and cayenne together in bowl. Add chicken and toss to coat. Cover and let stand at room temperature for 30 to 60 min.
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2. Rajas con creme: Char poblanos. Slice into 1/4-inch-thick strips. Adjust rack to middle and lowest, heat oven to 200.
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3. Heat oil in 12-inch nonstick skillet over high heat until just smoking. Add onion and cook until charred and just softened, about 3 minutes. Add garlic, thyme, and oregano and cook until fragrant, about 15 seconds. Add cream and cook, stirring frequently, until reduced and cream lightly coats onion, 1 to 2 minutes. Add poblano strips, lime juice, salt, and pepper and toss to coat. Transfer vegetables to bowl, cover, and place on middle oven rack. Wipe out skillet with paper towels.
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4. Remove chicken from marinade and wipe off excess. Heat remaining 1 tbsp oil in skillet over high heat until just smoking. Add chicken and cook without moving it until bottom side is well charred, about 4 minutes. Flip chicken; transfer skillet to lower oven rack. Bake until chicken registers 160, 7 to 10 minutes. Transfer to cutting board and let rest for 5 minutes; do not wash out skillet.
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5. Slice chicken crosswise into 1/4-inch-thick strips. Return chicken strips to skillet and toss to coat with pac juices. To serve, spoon few pieces of chicken into center of warmed tortilla, and top with spoonful of vegetable mixture, cilantro, and Spicy Pickled Radishes. Serve with lime wedges.
