Preheat oven to 425°. Combine 1 tablespoon extra-virgin olive oil, thyme, 1/4 teaspoon kosher salt, freshly ground black pepper, and sweet potatoes in a large bowl, tossing to coat sweet potatoes evenly. Place sweet potatoes on a jelly-roll pan, and bake at 425° for 16 minutes. Combine 1 tablespoon extra-virgin olive oil, 1/4 teaspoon kosher salt, crushed red pepper, and Broccolini in a bowl, tossing to coat Broccolini evenly. Remove sweet potatoes from oven, and stir. Arrange Broccolini on baking sheet with sweet potatoes; bake at 425° for 12 minutes or until Broccolini is crisp-tender and sweet potatoes are fork-tender.