Preheat oven to 400°F. Place beets in a 15x10x1-inch baking pan and drizzle with 2 tablespoons olive oil; toss to coat. Roast for 35 to 40 minutes or until very tender, stirring once. Remove from oven and let cool slightly.
Transfer cooled beets to a food processor. Add Greek yogurt, remaining 2 tablespoons olive oil, garlic, salt, and black pepper. Process until smooth, stopping to scrape sides as necessary.
Spread beet mixture onto toasted bread. Top with assorted seeds and chives.