Preheat oven to 400° F | 200ºC.
Heat olive oil in a medium skillet over medium heat. Add the leek leaves and cook, stirring, until the leaves are tender, about 3 to 5 minutes. Transfer to a 8 x 8-inch | 20 x 20 cm baking dish, covering the bottom and set aside.
In a small bowl stir together the water, tomato paste, herbs and salt and set aside.
Wash the vegetables and cut them into 1/4-inch | 0,5 cm rounds. Place them in the dish on top of the leek leaves, making alternating rows of vegetables until the dish is full. Vegetables should be fairly snug but not crammed into the dish.
Strain the herb broth over the vegetables. Season the vegetables with salt and pepper and finish with a drizzle of olive oil. Cover the dish with aluminum foil and bake until the vegetables are tender, about 40 minutes.
Remove the foil, top with grated cheese and bake, uncovered, until the topping is melted and golden, about 15 minutes. Let sit at least 10 minutes before adding the basil leaves and serving.