With a small, sharp knife, cut the oranges in half and rest the orange on the cut surface. Slice away strips of peels and the white membrane to expose the flesh all around the oranges.
Slice the oranges crosswise 1/8 to 1/4 inch thick.
Place the ball of burrata in the center of a serving plate and arrange the segments of orange around.
Drizzle generously with olive oil, season with salt and pepper, scatter over the torn mint leaves and serve.