Reserve fennel fronds and roughly chop. Trim both ends of fennel and discard outer leaves. Cut bulb in half then use a mandolin to thinly slice. Place slices in a bowl of iced water for 15 minutes.
Discard coarse outer green leaves of radicchio. Thickly slice radicchio and place in iced water with fennel.
Meanwhile, to make red wine vinaigrette, place all ingredients in a small bowl and whisk until combined.
Drain fennel and radicchio in a salad spinner and arrange in a large shallow serving bowl. Arrange beetroot wedges and cherries among leaves. Sprinkle with crumbled goat’s cheese, pine nuts, reserved fronds and chives. Spoon over vinaigrette and serve.