Pizza di Spaghetti

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2 large eggs

1/4 cup whole milk

1/2 cup grated Parmesan, plus extra for garnishing

Sea salt and freshly ground black pepper

2 cups leftover spaghetti with olives and tomato sauce, recipe follows

Spaghetti with Olives and Tomato Sauce:

1 pound dried spaghetti

1/4 cup olive oil

1 1/4 cups mixed olives, pitted and halved

1/2 tablespoon red pepper flakes, plus more if desired

3 cups tomato sauce, recipe follows

1/2 cup grated Parmesan

1/2 cup basil leaves, shredded

1/4 cup extra-virgin olive oil

Simple Tomato Sauce:

1/2 cup extra-virgin olive oil

1 small onion, chopped

2 cloves garlic, chopped

1 stalk celery, chopped

1 carrot, chopped

Sea salt and freshly ground black pepper

2 (32-ounce) cans crushed tomatoes

2 dried bay leaves

4 tablespoons unsalted butter, optional