Toast the walnuts in a dry skillet over medium heat. Remove to a plate and set aside.
Add 1/2 tablespoon extra-virgin olive oil, half a turn of the pan, and the onions. Cook for 5 minutes to soften, then put them in mixing bowl to cool.
While onions cool, put the milk, feta, half of the marjoram or oregano, mint, salt and pepper, to taste, and the nuts in a food processor and process to a thick, smooth sauce.
Add lamb to the bowl with the onions and season with salt and pepper, to taste. Stir in the remaining marjoram or oregano, paprika and cinnamon. Form the mixture into 4 patties, thinner at the center and thicker at the edges. Heat 1/2 tablespoon extra-virgin olive oil, in nonstick skillet over medium-high heat and cook the patties 3 to 4 minutes on each side for pink centers.
Meanwhile, heat 2 tablespoons extra-virgin olive oil in another skillet over medium-low heat. Add the garlic clove and let it infuse the oil for 1 to 2 minutes. Add the spinach and let it wilt, then remove the pan from the heat, and season with salt, pepper and nutmeg, to taste.
Add the lamb patties to the bun bottoms or charred bread. Shake off excess liquid as you remove the spinach and pile it on top of the burgers. Slather the bun tops with the feta sauce. Cover the burgers with the bun tops and serve.