Preheat oven to 425.
Place beets and butternut squash on 2 separate pieces of heavy duty foil. Drizzle each with 1 tablespoon extra virgin olive oil Sprinkle lightly with salt and pepper. Fold up foil around veggies to make 2 small packets and place packets on a sheet pan. Roast for 15 minutes, then remove squash. Open squash packet to let steam escapte and set aside.
Continue roasting beets for another 10-15 minutes or until fork tender. How long the beets take to bake depends on the size of the dice. When tender, remove beets from oven, open packet and set aside to cool slightly.
Combine lemon juice and garlic in a small bowl or jar. Stir with a whisk or a fork. Slowly add olive oil in a slow, steady stream while continually whisking. Add salt and pepper and stir well.
Combine quinoa, butternut squash, beets and herbs in a medium-large bowl. Stir gently to combine. Drizzle with half of the dressing and stir again. Taste and add more salt and pepper, if needed.
Scatter arugula and goat cheese over the top of the salad. Serve warm or at room temperature. Pass extra dressing in a small bowl or cruet at the table.