Peel the citrus and slice into rounds. Leave the white pith; it helps keep the citrus intact when cooking. Lay out citrus rounds on an oiled baking sheet.
Broil the citrus on high for approximately 5 minutes. Depending on the oven, this may be quicker or slower, so watch it closely every 30 seconds. Take it out when the edges of the fruit are just slightly tinged dark brown.
Let the fruit cool for 5 minutes, then move each citrus round to a platter with a spatula. Sprinkle with the feta, mint, olive oil and salt. Serve immediately or at room temperature.