1 large ruby-red grapefruit or 3 blood oranges
2 small fresh fennel bulbs, trimmed, halved vertically, sliced paper-thin
1 cup fresh Italian parsley leaves
1/4 cup fresh mint leaves
Extra-virgin olive oil
Sea salt flakes
Cut off top and bottom ends of grapefruit.
Stand on 1 flat side.
Starting at top of fruit, cut off all peel and white pith, following curve of fruit.
Working over bowl, cut between membranes, releasing segments; squeeze any juice into bowl.
Transfer segments to another bowl. DO AHEAD: Can be made 1 day ahead.
Cover juice and segments separately and chill.
Combine fennel and herbs in large bowl.
Cut grapefruit segments into 1/3- to 1/2-inch cubes.
Add to bowl with fennel and toss to coat.
Arrange salad on platter.
Drizzle lightly with oil, then grapefruit juice, if desired.
Sprinkle with sea salt flakes and serve.