In a large saucepan, bring 3 cups water, the bulgur and 1/2 teaspoon salt to a boil; lower the heat, cover and simmer until tender, 10 to 12 minutes; transfer to a bowl. Toss with 3 tablespoons olive oil, the finely chopped onion, parsley, chopped oregano and lemon juice. Season with salt and pepper and refrigerate until ready to serve.
Using a food processor, pulse the onion quarters, oregano leaves, lemon peel, tahini and 1/2 teaspoon salt. With the machine on, add 2 tablespoons olive oil and process until smooth; transfer to a medium bowl. Add the chicken and toss.
In a shallow dish, whisk together the flour, sesame seeds and 1/4 teaspoon salt. In a large nonstick skillet, heat 3 tablespoons olive oil over medium-low heat. Working in batches, and using the remaining olive oil as needed, coat the chicken cutlets in the sesame flour. Add to the pan and fry, turning once or twice, until golden-brown and cooked through, about 5 minutes. Serve with the tabbouleh.