In a 9 in medium skillet or cast iron pan, heat butter or oil over medium heat. Sauté onion until translucent, about 5 minutes. Add asparagus and cook for 2 to 3 minutes, until tender and bright green.
In large bowl, whisk eggs with milk, chives, mint, salt, and pepper. Pour into pan with asparagus and cook over medium heat, stirring to begin cooking eggs, for 2 to 3 minutes. Remove from heat and dot the top with cheese.
Transfer frittata to oven and bake until eggs are set and beginning to brown on top, about 10 to 15 minutes. Using an oven mitt (the handle will be very hot!), remove frittata from oven. Slice into wedges and serve with a fresh salad.