►Cook spinach in a large skillet over medium heat until wilted, about 5 minutes. Transfer wilted spinach to a colander and drain for 15 minutes. Once cool enough to handle, squeeze spinach to extract any remaining liquid.
►Combine squeezed spinach, ricotta, eggs, 1 cup flour, and 1½ cups ricotta salata in a food processor and process for 1 minute. Transfer mixture to a large bowl and add remaining 2 cups flour, salt, and pepper. Stir to combine.
►Lightly dust a work surface with flour. Roll dough into roughly ¾-inch-wide, 15-inch-long logs. Using a butter knife, cut logs into ¾-inch pieces and transfer to floured surface.
►Fill a large pot with water and bring to a boil. Reduce heat to medium and gently poach gnocchi for 5 to 6 minutes. Remove using a slotted spoon and place on a rimmed baking sheet. Do not overcrowd or gnocchi will stick together.
►Melt butter over medium heat in a large skillet. Continue cooking until browned and nutty, about 7 minutes total. Toss gnocchi with browned butter, prosciutto, and remaining ½ cup ricotta salata. Season to taste and serve immediately.