Place all the dressing ingredients in a bowl and whisk to combine. You may need to whisk again before drizzling over the salad to make sure the oils and vinegars are well combined. They will separate if left alone too long.
Assemble the salad:
Place the radicchio, arugula, celery, apples, apricots, and dill in a large salad bowl. Sprinkle with salt and pepper.
Drizzle the dressing over the salad and toss to combine. Taste and adjust seasoning.