How to Make It
Place basil, poblano, stock, jalapeño, vinegar, juice, 1/4 teaspoon salt, sugar, garlic, and 3 green onions in the bowl of a food processor; process until finely chopped.
Heat a large skillet over medium-high. Add oil; swirl to coat. Sprinkle chicken evenly with remaining 1/2 teaspoon salt and black pepper. Add chicken to pan; cook 5 minutes. Turn chicken; cover, reduce heat to medium, and cook 8 minutes. Add basil mixture to pan; bring to a simmer. Cook, uncovered, 5 minutes. Place chicken on a platter; drizzle with basil mixture. Thinly slice remaining green onion; sprinkle over top.