Preheat the oven to 425 F. Toss together beets, olive oil, salt, and pepper and arrange in a single layer on a baking dish. Add 1/4 cup water and cover tightly with foil. Bake until the beets are tender, about 30 minutes.
Remove the foil and continue to bake until the water has evaporated and the beets are slightly caramelized, about 15 minutes more.
Drizzle the cooked beets with balsamic glaze and combine goat cheese, nuts (if using), and arugula. Serve immediately.