For mint sauce, combine vinegar, caster sugar and 2 tbsp water in a small saucepan over medium heat. Bring to the boil, stirring to dissolve sugar. Remove from heat, cool slightly, stir in mint, season to taste and set aside.
Preheat oven to 180C. Combine oil, garlic, rosemary and half the lemon rind in a bowl. Add chops, turn to coat and season to taste.
Heat a large char-grill pan over medium-high heat. Add chops and cook, turning once, until golden (1-2 minutes each side). Transfer to an oven tray lined with baking paper and roast in oven until cooked to your liking (5-6 minutes for medium). Cover loosely with foil and set aside in a warm place to rest (5 minutes).
Cook peas in boiling salted water until bright green (1-2 minutes), then drain, reserving 40ml cooking water. Return peas to pan with reserved water, butter and remaining lemon rind, coarsely crush with a fork and season to taste. Serve hot with Barnsley chops and mint sauce.