In a 10-inch cast-iron skillet, melt butter over medium-high heat. Add onion; cook for 5 minutes, stirring frequently. Add asparagus; cook 2 minutes. Remove from heat. Place onion mixture into a large bowl and wipe skillet clean.
In the container of a blender, combine eggs, half-and-half, salt, and pepper; process until smooth. Add egg mixture to onion mixture, stirring to combine. Add 1 cup arugula and 1 cup tomato.
Bake until set, 14 to 16 minutes. Let cool for 10 minutes.
In a small bowl, toss remaining 1 cup arugula, remaining ½ cup tomato, and oil together until well coated. Sprinkle mixture over frittata. Garnish with pepper, if desired.
Recipe by Southern Lady Magazine at https://southernladymagazine.com/arugula-and-tomato-frittata/