Pre-heat oven to 350 degrees F. Grease a 9 x 9 casserole dish with oil and set aside.
Heat a large sauté pan over medium heat. Add a tablespoon of oil and leeks with 1/4 teaspoon salt. Immediately turn heat to medium-low. Sauté, stirring often until slightly browned and translucent, about 10-15 minutes.
Shred up the remaining vegetables with a hand grater or food processor- potato, sweet potato, onion, zucchini, and garlic and remove as much water as you can with paper towels. This is important for a dry kugel! Combine with leeks, eggs, ¼ cup vegetable oil, matzo meal, remaining salt and pepper in a large bowl. If is very wet, add in a little more matzo meal.
Pour mixture into the casserole dish, smooth over with a spatula, and bake for 45 minutes until kugel is cooked through and topping is browned.
Let cool slightly, cut into squares and eat!