Segment the grapefruit over a bowl to catch any juices and squeeze excess juice from the membranes.
Use 1/4 cup of this juice for the dressing, whisking it with the olive oil, sesame oil, maple syrup, a pinch of white pepper (about 2 ground peppercorns or 1/16 teaspoon), and a pinch of sea salt. Taste and adjust seasonings, if desired.
Gently toss the fennel and pea shoots in half of the dressing. Arrange on two plates, top with the grapefruit and avocado, and drizzle the remaining dressing over the fruit.