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.
While the burgers are cooking, place a small pot over medium heat with the butter. Sprinkle the flour over the melted butter and cook, stirring frequently, for about 1 minute. Whisk the milk into the butter-flour mixture then stir in the ricotta, Parmigiano Reggiano, some salt and pepper. Bring up to a bubble and simmer until thickened, about 2 minutes.
Serve the burgers on the ciabatta buns topped with a hearty ladleful of cheese sauce and a sprinkle of shredded spinach. Serve with Squashed Rosemary Potatoes and Tomato and Spring Onion Salad alongside.