1. In a pot with a steamer basket, steam the beets until tender, about 12 minutes. Transfer beets to a large bowl and toss with 2 tablespoons each of the oil and vinegar; mix in the garlic, salt and sugar. Let sit at room temperature at least 30 minutes.
2. Meanwhile, in another pot, bring the 2 cups water to a boil. Stir in the quinoa and a pinch of salt. Cover and cook over medium-low heat until water is absorbed, about 15 minutes. Fluff quinoa with a fork and let cool.
3. In a small skillet over medium heat, warm remaining oil. Add the pine nuts and cook, stirring, until golden, about 3 minutes. Pour pine nuts and oil over quinoa and toss.
4. Remove garlic from beets. Add quinoa and the arugula and cheese to beets and toss well. Season with vinegar, salt and black pepper to taste. Serve chilled or at room temperature.