Place a medium skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the onion and garlic to the pan, and cook until tender, 4-5 minutes. Turn the veggies out into a large mixing bowl, add the defrosted spinach and nutmeg, and toss to combine. Add the ground meats, some salt and pepper to the bowl, and mix to thoroughly combine. Form the mixture into 4 equal patties and reserve.
Place a large skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons, and the whole sprig of rosemary. Add the burgers to the hot pan and sear until golden brown and cooked through, 4-5 minutes per side.