1. Score fat side of meat in a diamond pattern, making ½-inch-deep diagonal cuts ½ inch apart. Rub beef on all sides with 2 tablespoons salt (wash hands); let rest at room temperature 30 minutes.
2. Preheat grill on medium-low. Place beef fat-side up on grill, close lid, and cook 25–35 minutes, rotating occasionally (do not flip), until beef is 115°F.
3. Meanwhile, halve zucchini and bell peppers lengthwise; cut sweet onion into 1-inch-thick rings. Combine zucchini, bell peppers, sweet onions, mushrooms, and green onions in large bowl; add ⅓ cup garlic vinaigrette and 1 teaspoon salt and toss to coat.
4. Chop parsley coarsely (1 cup). Combine parsley, vinegar, and remaining 1 cup garlic vinaigrette and ½ teaspoon salt; set parsley dressing aside.
5. Uncover grill and increase to medium-high. Flip beef onto fat side and cook 6–10 minutes, rotating often to avoid flare-ups, until fat cap is rendered and charred and beef is 125°F (for medium rare; warm red center), 130°F (for medium; warm pink center), or up to 170°F (for well done). Remove beef from grill and let rest 20 minutes; temperature will rise 5–10°F during this time.
6. Place zucchini, bell peppers, sweet onions, mushrooms, and green onions on grill; cook 8–10 minutes, flipping occasionally, until charred and crisp-tender. Chop green onions finely and stir into parsley dressing. Cut remaining grilled vegetables into 1-inch pieces and place in large bowl; add ½ cup parsley dressing and toss to coat.
7. Slice beef against the grain; serve with vegetable salad and remaining parsley dressing.

Chef's Tip: Picanha has a large fat cap that can cause flare-ups while cooking. Move or rotate beef if flare-ups occur, reducing heat if necessary.