Preheat the oven to 400 degrees. Arrange the bread on a baking sheet. In a medium skillet, melt the butter with the EVOO, 2 turns of the pan, over medium heat. Add the onion and garlic and cook until softened, about 5 minutes; season with salt and pepper. Whisk in the flour for 1 minute, then whisk in the milk and season with the nutmeg. Cook until thickened, about 5 minutes.
Pull the spinach apart, then add to the sauce. Fold in the artichokes and cook until heated through. Stir in the parmigiano-reggiano, season with salt and remove from the heat.
Spread the spinach and artichoke mixture on the bread and top with the mozzarella. Bake until the cheese is melted, 10 to 12 minutes. Top with the thyme.