Preheat oven to 350F.
Arrange bread on a baking sheet and bake until lightly toasted. Transfer to a large mixing bowl. Turn off oven.
Chop vegetables and heat a large skillet with EVOO, 4 turns of the pan, over medium-high heat. Add garlic, onions, carrots and celery, and sweat veggies a few minutes. Wilt in the kale or add the spinach. Season with nutmeg, oregano or marjoram, thyme, rosemary, salt and pepper. Cook 8-10 minutes to tender. Stir in tomato paste, cook 1 minute then add stock and simmer 5 minutes over medium-low heat.
Pour mixture over bread, add a few handfuls of cheese, about 3/4 cup. Toss to combine, transfer to a baking dish and cool.
Beat eggs with milk, salt and pepper. Pour eggs over cooled bread casserole, cover and chill overnight or a minimum of a couple of hours.
Heat oven to 400F. Top the casserole with a drizzle of EVOO and remaining cheese. Bake until puffed and golden, 45 minutes.