Combine yogurt, vinegar, chile, adobo sauce and 1 pinch each salt and pepper in a blender; blend until smooth. With blender running, add olive oil in a slow stream, blending until thickened and emulsified, for dressing. Transfer to a bowl and set aside.

Cut each cutlet crosswise in half. Place each between 2 sheets of plastic wrap and pound gently with a meat mallet or rolling pin to 1/4-inch thickness. Whisk together egg and juice in a shallow bowl. Combine bread crumbs, chili powder and 1 pinch salt in another shallow bowl. Dip cutlets, 1 at a time, in egg mixture (allowing excess to drip back into bowl), then in bread crumbs, turning to coat well. Transfer, as coated, to a large plate.

Heat 1 tablespoon vegetable oil in a large nonstick skillet over moderately high heat until hot but not smoking. Add cutlets, in 2 batches (wiping pan with a paper towel between batches and adding remaining 1 tablespoon oil to second batch), and cook, turning once, until golden brown and cooked through, about 3 minutes. Transfer, as cooked, to a serving platter; drizzle with some dressing.

Gently toss together beans, greens and 3 tablespoons dressing in a large bowl until coated. Serve with cutlets and remaining dressing on the side.