Place the mustard, lemon juice, salt, and pepper in a small bowl. Slowly whisk in the olive oil until the vinaigrette is emulsified.
Before serving, cut the avocados in 1/2, remove the seeds, and carefully peel off the skin. Cut each half into 4 thick slices. Toss the avocado slices in the vinaigrette to prevent them from turning brown. Use a large, sharp knife to slice the peel off the grapefruits (be sure to remove all the white pith), then cut between the membranes to release the grapefruit segments.
Arrange the avocado slices around the edge of a large platter. Arrange the grapefruit segments in the center. Spoon the vinaigrette on top, sprinkle with salt and pepper, and serve.
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