Wash the fennel bulb, slice thinly (1/8-inch thick), and reserve fronds for garnish. This takes about 5 minutes.

Segment the grapefruit by removing the peel and white pith, exposing juicy segments. Set segments aside.

Cut the avocados in half, remove the pit, scoop the flesh, and slice into chunks. This should take around 5 minutes.

In a large mixing bowl, combine fennel, grapefruit segments, avocado chunks, and lightweight greens. Toss gently.

To make the dressing, mix grapefruit juice, olive oil, balsamic vinegar, minced shallot, mustard, salt, and pepper in a jar. Shake until blended.

Drizzle the dressing over the salad mixture, toss gently to combine, and adjust seasoning if necessary.

Transfer the salad to a serving dish and garnish with reserved fennel fronds and shaved parmesan. Serve immediately.