In a microwaveable bowl, defrost the spinach in the microwave for 6 to 8 minutes. Drain the spinach in a kitchen towel and wring dry. Tear the spinach into small pieces and set aside.
In a medium skillet, melt the butter over medium heat. Add the garlic and onion and cook until tender, about 5 minutes. Stir in the thyme and lemon peel. Whisk in the flour and cook for 1 minute. Gradually whisk in the chicken broth and season with salt, pepper and the nutmeg. Increase the heat to high and cook, whisking often, until thickened, 6 to 8 minutes. Stir in the spinach, artichokes and half each of the Parmigiano-Reggiano and the mozzarella. Transfer the mixture to a casserole. Sprinkle the remaining cheese on top.
Preheat the broiler. Broil the dip until bubbly and lightly browned, about 3 minutes. Serve with the bread cubes.