Heat oven to 425 degrees F with a rack in center of oven.
In a large bowl, toss cubed beets with olive oil, orange juice and salt; transfer to a rimmed sheet pan and spread in an even layer.
Roast 30 minutes, shaking and rotating pan halfway through baking, until beets are softened and are starting to caramelize.
Sprinkle shallots over beets and return to oven. Roast 15 minutes until shallots are golden brown and beets are fork-tender.
Transfer beet-shallot mixture to a large bowl; while still warm, toss with oranges, pistachios, feta cheese and chives to combine. Drizzle with extra olive oil and sprinkle with ground black pepper.
Serve warm, room temperature or chilled. Salad keeps stored in an airtight container in the fridge for up to 4 days.
Notes
From Sheet Pan Suppers: 120 Recipes for Simple, Surprising, Hands-Off Meals Straight from the Oven by Molly Gilbert