Pickle the Onion: In a small bowl, mix sugar with 4 tablespoons of vinegar. Add the sliced red onion and let it sit for 15 minutes. Drain the onion and set aside, reserving the vinegar.

Prepare the Oranges: Peel the blood oranges and slice them into rounds. Collect about 2 teaspoons of juice from the cutting board for the dressing. If needed, squeeze a few slices to get enough juice.

Make the Dressing: In a jar or small bowl, combine 2 teaspoons of the reserved pickling vinegar, 2 teaspoons of blood orange juice, 2 tablespoons of olive oil, and a pinch of salt and pepper. Shake or whisk well.

Dress the Fennel: In a large bowl, toss the sliced fennel with 1 tablespoon of the reserved pickling vinegar, the remaining 2 tablespoons of olive oil, 1/4 teaspoon salt, and 1/8 teaspoon pepper.

Assemble the Salad: Arrange half of the orange slices on a serving platter. Layer with two-thirds of the dressed fennel, then add some of the pickled onion and parsley. Add the remaining orange slices and fennel. Top with the rest of the onion and parsley.

Finish and Serve: Just before serving, drizzle the blood orange dressing over the salad, focusing on the oranges to avoid staining the fennel. Serve immediately.