Sauté zucchini in 1½ tablespoons olive oil over medium-high heat until it begins to brown but is still firm, about 10 minutes. Season with salt and set aside.
In a medium saucepot, sauté onion and leeks in remaining olive oil over medium heat until they begin to brown, about 5 minutes. Add garlic and cook another minute before adding tomato paste and tomatoes.
Add 2 cups water and salt to the onion mixture, increase heat, and bring to a slow boil. Stir in the bulgur, reduce heat to a simmer, and cook until bulgur is tender and the liquid has been absorbed, another 12 to 15 minutes. Remove from heat and stir in zucchini and chopped mint and parsley.
To serve, put in a large bowl and top with goat-milk feta, crumbled, and whole mint and parsley leaves.