1. Heat a grill to high (450° to 550°). Rub peppers with 1 tbsp. oil. Grill peppers, turning often, until charred all over, about 10 minutes. Put in a bowl and cover with a towel to steam.
2. Meanwhile, mix 2 tbsp. oil, the vinegar, salt, and sugar. Slice cheese and set on a serving plate.
3. Peel peppers, stem, and slice; discard skins. Mix peppers with vinegar mixture and spoon over cheese. Drizzle with remaining 1 tbsp. oil and sprinkle with the oregano. Serve with bread.