Preheat oven to 400 degrees F. In a heavy skillet or cast-iron pan, heat 1 tablespoon olive oil over medium-high heat. Add tomato paste, eggplant, and onion. Sauté for 3 to 5 minutes. Turn down heat, stir in garlic, and cook for another 1 to 2 minutes. Add tomatoes, red pepper flakes, vinegar, and basil. Season with salt and pepper and simmer for 10 to 12 minutes.
Stir in farro pasta, remove from heat, and arrange pieces of feta on top. Bake for 10 minutes, until the cheese is golden brown and bubbly. Garnish with parsley and lemon zest, if desired.