Submerge the sliced shallot in a bowl of ice water and let stand for 30 minutes to remove the harsh sulfurous bite. Drain the rings and pat them thoroughly dry with paper towels.

Grate the zest from the oranges until you have about a teaspoon, then set it aside. Use a sharp knife to cut away the peel and white pith from the fruit; quarter the oranges and slice them crosswise into thin pieces.

Whisk the orange zest, vinegar, garlic, mayonnaise, paprika, and a portion of the salt together in a medium bowl. While whisking constantly, drizzle in the oil in a slow stream until the dressing is thick and emulsified.

Toss the sliced avocados gently with two tablespoons of the dressing and the remaining salt in a separate bowl. Transfer the seasoned avocado to a large platter, spreading it out into an even base.

Combine the soaked shallot, orange slices, fennel, toasted almonds, and parsley in the bowl with the remaining dressing and toss to coat every piece. Spoon the citrus mixture over the avocado base.

Sprinkle the chopped olives over the top and serve immediately while the fennel is still crisp.