First, prepare the vinaigrette.
In a small bowl, combine ¼ cup (60 ml / 2 fl oz) of the blood orange juice, 3 tablespoons (45 ml / 1.5 fl oz) of the olive oil, and the blood orange segments.
Set aside to marinate for at least 15 minutes.
While the vinaigrette marinates, prepare the hearts of palm.
Slice them crosswise into very thin rounds, about ⅛-inch (3mm) thick.
Season the slices with salt and grains of paradise to taste, and rub gently with 3 tablespoons (45 ml / 1.5 fl oz) of the olive oil.
In a separate small bowl, toss the shaved fennel with the remaining ¼ cup (60 ml / 2 fl oz) blood orange juice, the remaining 2 tablespoons (30 ml / 1 fl oz) olive oil, and a pinch of salt.
To assemble, create a small mound of the shaved fennel salad in the center of each of 4 serving plates. Artfully layer the hearts of palm slices over and around the fennel.
Spoon a few of the marinated orange segments around the hearts of palm, and drizzle each plate with about 2 tablespoons (30 ml / 1 fl oz) of the blood orange vinaigrette.
Garnish with a sprinkle of fennel pollen, a few more grinds of grains of paradise, and the fresh lemon thyme leaves.
Serve immediately.