Preheat the oven to 450 degrees F. Arrange two oven racks evenly spaced.
Place the beets on a sheet pan, toss with 2 tablespoons olive oil, 1/2 teaspoon salt, and 1/2 teaspoon pepper, and spread out in one layer. On a second sheet pan, toss the butternut squash and apples with 2 tablespoons olive oil, 1 teaspoon salt, and 1/2 teaspoon pepper and spread out in one layer. Roast both pans of vegetables for 25 to 30 minutes, tossing occasionally, until everything is tender and lightly browned.
Meanwhile, for the vinaigrette, heat 1/3 cup olive oil in a small saute pan over medium-low heat. Add the shallot and cook for 3 minutes. Add the garlic and cook for 30 seconds. Over low heat, whisk in the balsamic vinegar, orange zest, orange juice, honey, mustard, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Keep warm.
Place the roasted vegetables and fruit in a large bowl. Add the arugula and vinaigrette and toss well. Sprinkle with the almonds and serve warm.