Make aioli by adding all of the ingredients in a bowl and whisk together until fully combined. Adjust ingredients to desired taste. Set aside in the refrigerator until you are ready to use.
Next, dice your cold, leftover baked potatoes into medium-sized cubes (about 1 inch). Be sure to include the skin as it will get crispy.
Next, in a large skillet (cast iron is ideal), heat the olive oil over medium-high heat until hot.
Add the diced potatoes in a single layer. Let them sit without stirring for 3–4 minutes so they develop a crispy crust. Flip or stir gently, and let them crisp up on the other sides, about 10-14 minutes total (cooking time will vary based on desired crispiness).
Next, liberally season the potatoes with salt and pepper. I typically place my potatoes in a metal mixing bowl to season to ensure the seasoning is evenly coated. Note, you want to season the home fries straight while they are hot.
Lastly, garnish with chives and serve with aioli and ketchup.