Adjust the oven rack to the upper-middle position. Heat broiler.

In a medium bowl, whisk eggs, half-and-half, salt, and pepper. Set aside.

In a 10-inch cast iron or other ovenproof skillet, heat vegetable oil over medium heat. Add potatoes to the skillet, and cook, stirring occasionally, until golden brown and just tender enough to pierce with a fork, about 15 minutes. Remove potatoes from pan, add more oil if necessary, and add asparagus. Cook, stirring constantly, until lightly browned, about 3 minutes. Add shallot, and cook until shallot softens slightly, about 2 minutes. Mix potatoes back into the skillet.

Stir feta and mint into egg mixture, and add mixture to skillet. Reduce heat to mediumlow, and cook, constantly stirring, scraping the bottom of the skillet, until large curds form but the eggs are still very wet, about 5 minutes. Shake to distribute the mixture, and cook another 30 seconds to set the bottom of the frittata.

Slide the skillet under the hot broiler, and cook until the frittata has puffed and the top is spotty brown. Depending on the heat of your broiler, this will take between 1 and 3 minutes. Remove the skillet from the broiler, and let stand on a cool burner for 2 minutes to set up and begin to cool.

Using a flexible metal spatula, remove the frittata from the skillet. Cut into wedges and serve, garnishing with additional mint, feta, or chives.