Preheat the oven to 400 degrees F.

Rinse vegetables well, and dry with a paper towel. Slice potatoes and squash very thinly about 1/8-inch thick. Use a mandolin if available, as it will vastly reduce the cooking time as well as produce evenly cooked vegetables.

Slice leek vertically down the center. Take one half and wash thoroughly to remove sand and dirt between the layers. Dry with a paper towel and slice starting from the white end up until needed quantity is reached.

Add sliced vegetables to a large casserole dish and toss with olive oil, chopped rosemary and basil. Remove 2/3 of the mixture back onto the cutting board and arrange the remaining 1/3 evenly over the bottom of the casserole dish.

Sprinkle with 1/2 of the goat cheese, salt and pepper to taste.

Spread another 1/3 of the vegetable mixture evenly over the goat cheese. Sprinkle the remaining goat cheese, salt and pepper to taste.

Spread the remaining 1/3 of the vegetable mixture evenly over the goat cheese. Pour milk over the casserole dish, and evenly sprinkle the shredded Pecorino Romano over the vegetables.

Cover and bake on the middle rack for 30-35 minutes. Uncover and cook for 15 minutes longer. For a browned top put the oven broiler on high for about 3 minutes to achieve a brown crust on top of the casserole.