Preheat oven to 400°F. Toss beets and apples with olive oil, salt, and pepper on a baking sheet.
Roast 30–35 minutes until beets are tender; let cool slightly, then peel beets if desired.
In a saucepan, sauté onion until translucent, add garlic for 1 minute.
Add roasted beets, apples, and broth. Simmer 10 minutes to meld flavors.
Use an immersion blender (or transfer to a blender) and puree until smooth.
Stir in grated horseradish; adjust salt and pepper. Reheat gently.
Serve with a dollop of Greek yogurt and sprinkle of dill or chives.