Scrub beets and put in a baking pan large enough to arrange them in a single layer.
Sprinkle with 1 tsp. salt. Cover with foil and roast until tender when pierced with the tip of a small, sharp knife, about 1 hour.
Cool beets until cool enough to handle. Peel and cut into 1/2-in.-thick wedges.
Combine pea shoots, shallot, chives, oil, lemon juice, and remaining 1/2 tsp. salt in a large bowl. Top with beets, avocados, and pepper, tossing just to coat.
Make ahead: Roasted beets, up to 1 day (peel and slice just before making salad).
