Preheat oven to 350 degrees F (175 degrees C). Brush a pie plate with 1 tablespoon olive and dust with 1 tablespoon Parmigiano-Reggiano cheese.
Heat remaining olive oil in a large skillet over medium heat. Cook and stir leeks with a pinch of salt in hot oil until leeks are soft and sweet, 5 to 10 minutes. Stir garlic into leeks and cook until fragrant, about 1 minute.
Stir leek mixture, rice, spinach, 3/4 cup Parmigiano-Reggiano cheese, eggs, salt, black pepper, cayenne pepper, and nutmeg together in a bowl. Transfer spinach-rice mixture to the prepared pie dish and smooth the surface with a spatula; dust the top with remaining 1 tablespoon Parmigiano-Reggiano cheese.
Bake in the preheated oven until torta is lightly browned around the outside and firm to the touch, 35 to 40 minutes.