In a blender combine all ingredients for the vinaigrette. Process until shallot is completely pureed. Pour into a mason jar to save for later.
Preheat a cast iron grill pan to high heat.
Place plum pieces on the grill pan in a diagonal pattern and sear for 1-2 minutes, or until black grill marks are evident. Flip and repeat on the opposite side. (Note- I had to do this in 2 batches for all the plums).
Set plums aside.
In a large mixing bowl combine the arugula and about half of the dressing. Toss to coat. Sample the greens and add more dressing, to taste.
Plate onto 4 separate salad places. Evenly distribute the almonds, feta, and dried apricots between the salads.
Arrange 5 plum pieces around each plate in a star pattern.