Preheat oven to 375°F. In a large bowl, combine spinach, rice, milk, eggs,1/4 cup cheese, 1 1/2 teaspoons salt, and 1/4 teaspoon pepper. In a large skillet, heat oil over medium-high. Add onion and garlic and season with salt and pepper. Cook, stirring occasionally, until onion is soft and beginning to brown, about10 minutes. Add wine and cook until evaporated, about 3 minutes. Add ham and cook until warmed through, about 2 minutes.

Add ham mixture to spinach and stir to combine. Transfer to an 8 inch square baking dish; top with 1/÷cup cheese. Bake until warmed through and golden brown on top, 25 to 30 minutes.