Cook the shallots in butter: Heat the butter in a 10-inch oven proof frying pan over medium heat. Add the shallots and cook, stirring occasionally, until they soften and turn translucent, about 3 minutes.
Add the asparagus: Add the sliced asparagus and cook for an additional 3 minutes.
Add the egg mixture: Beat the eggs, ricotta cheese, and salt together. Pour the egg mixture into the pan and cook until almost set, but still runny on top, 4 to 5 minutes. While cooking, preheat the oven broiler.
Top with cheese and broil: Sprinkle Gruyere cheese over the eggs and put in the oven to broil until the cheese is melted and browned and the center is set, about 6 to 8 minutes. Remove the pan from the oven with oven mitts and slide the frittata onto a serving plate. Cut into wedges.