Place the chopped sweet potato in a microwave-safe bowl. Fill the bowl with water to a depth of 1/2 inch. Cover the plate with a paper towel (or use a reusable microwave-safe cover). Microwave on high until the cubes are slightly tender but not fully cooked, about 4 to 5 minutes. Let cool a few minutes, then drain.
Meanwhile, heat 2 tablespoons oil in a 10-inch cast-iron or similar ovenproof skillet over medium-high heat. Swirl to coat the skillet. Once the oil is hot, add the ham. Cook, stirring often, until the ham is browned on all sides, 4 to 5 minutes. With a slotted spoon, remove the ham to a plate and set aside.
Place the skillet in the oven. Broil until the eggs are set and the top is golden, about 3 to 5 minutes. Watch very carefully towards the end of the cooking time to ensure it doesn’t burn (don’t walk away!). This time may vary depending upon your skillet (different materials hold heat differently). If at the 5 minute mark your frittata is not fully cooked, switch the oven to BAKE at 350 degrees F and continue cooking until the eggs are set. Remove from the oven (be careful, the skillet handle will be hot). Let cool a few minutes. Slice and serve warm or at room temperature.
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