Using a food processor, finely chop the garlic. Add the parsley, 1/4 cup olive oil, the onion, thyme, vinegar, mustard seeds, 1 teaspoon salt and 1/2 teaspoon pepper and pulse to combine. Coat the steak with 2 tablespoons of the chimichurri sauce and let stand at room temperature for 15 minutes. Meanwhile, preheat a grill for both high and medium heat.
In a large bowl, toss the sweet potatoes with the remaining 1/4 cup olive oil; season with salt and pepper. Arrange on an oiled grate over medium heat, cover and grill, turning occasionally, until tender, 15 to 20 minutes.
Meanwhile, arrange the steak on the oiled grate over high heat, cover and grill, turning once, for 8 to 10 minutes for medium-rare. Transfer to a work surface and let rest for 10 minutes before thinly slicing. Serve with the remaining chimichurri and the sweet potatoes.