To make it simple, you can use a cast iron skillet or an oven-safe cooking pan. Or, you can use two pans.
Preheat a cooking pan over medium-high heat and add some vegetable oil for cooking. Add diced yellow onion and ham and cook, stirring often, until you get some caramelization.
Stir in 1/2 Tbsp honey mustard and cook for another minute. Take ham and onions out of the pan and set aside.
Add a little more vegetable oil to the pan and diced potatoes. Add some salt and pepper. Cook potatoes over medium heat, covered, until almost cooked. Take off the lid and let the potatoes cook until just done. Stir in 1/2 Tbsp honey mustard.
Preheat oven to 400.
Add ham and onions to the potatoes. (If not using an oven-safe cooking pan, then transfer ham and potatoes into an oven safe dish.)
Crack eggs over ham and potatoes. Bake for 10-15 minutes.