1. To prepare tomatoes, preheat oven to 250°.
2. Combine tomatoes, 2 tablespoons olive oil, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a large bowl; toss to coat. Arrange tomatoes in a single layer on a foil-lined baking sheet. Bake at 250° for 3 hours or until very tender, stirring every hour.
3. To prepare cakes, combine zucchini and 1/2 teaspoon salt in a cheesecloth-lined bowl. Let stand 10 minutes. Gather edges of cheesecloth; squeeze zucchini in cloth until barely moist. Combine zucchini, 1/2 teaspoon salt, farro, and next 7 ingredients (through garlic) in a large bowl. Let stand 5 minutes. Shape mixture into 12 (3-inch) patties, about 3/4 inch thick.
4. Heat 2 teaspoons oil in a large skillet over medium heat. Add 4 patties; cook 4 minutes on each side or until golden. Repeat in two more batches with remaining oil and patties. Keep warm.
5. To prepare cheese, combine cheese and remaining ingredients in a small bowl, stirring until well combined.
6. Arrange 2 zucchini cakes on each of 6 plates. Top with 1 tablespoon cheese mixture and 1/4 cup tomatoes.