To make the dough: In a large bowl, mix together flour, salt and sugar to combine. Mix in cubed butter with your hands, pinching and squeezing the butter cubes (or use a pastry blender or food processor) until the largest pieces are the size of lima beans. Drizzle in the water a little at a time, mixing until the dough starts to come together into a mass. You may not need all the water, or you may need to add more.
When dough is starting to hold together but is still somewhat crumbly, transfer it to a lightly floured surface and press and knead it together into a smooth ball. Flatten into disk, wrap in plastic wrap and chill for 1 hour.
While dough chills, heat oven to 400 degrees.
To prepare vegetables: On a rimmed baking sheet, toss together eggplant, 1/4 cup oil, 2 garlic cloves, 1 1/2 teaspoons rosemary, 1 1/2 teaspoons thyme and 1/4 teaspoon salt.
On a second rimmed baking sheet, toss together the cherry tomatoes, onion slices, 2 tablespoons oil, 2 garlic cloves, 1 teaspoon rosemary, 1 teaspoon thyme and 1/4 teaspoon salt.