Preheat oven to 450°F. Line a baking sheet with foil. Mix bread crumbs, 2 Tbsp. Parmesan, 1/2 tsp. salt and 2 Tbsp. oil in a shallow bowl. Brush chicken on both sides with 1 Tbsp. oil and dredge in bread crumb mixture. Transfer to prepared baking sheet. Sprinkle remaining crumb mixture over chicken. Roast until chicken is opaque and crumbs are golden, 7 to 10 minutes.
Arrange romaine halves around chicken. Brush with 1 Tbsp. oil. Return sheet to oven; roast until outer leaves have wilted and chicken is cooked through, about 5 minutes.
Whisk remaining 1/4 cup oil with mustard, yogurt, lemon juice, anchovies and garlic. Arrange romaine and chicken on plates, drizzle with dressing and sprinkle with remaining Parmesan, and serve.