Heat large skillet to medium-high heat, add 2 tablespoons of butter (or ghee), and let it melt, swirling to coat the pan.
Add 1/2 the onions and let reduce for 2 minutes, stirring fairly constantly.
Add potatoes and stir to coat. Cover and cook potatoes, uncovering to stir often, continue cooking on medium heat for approximately 10-15 minutes, adding the additional tablespoon of butter, as needed, to ensure the potatoes don't dry out or stick to the pan.
Add remaining onion, salt and pepper. Mix to combine and cook another 5 minutes and then start testing the potatoes for taste and firmness. Add additional salt and pepper as needed.
Once the potatoes have reached your desired firmness, serve immediately with ketchup of your choice and an over-easy egg.
Notes
Paleo/Whole30: if you are concerned with paleo/Whole30 use ghee instead of butter and serve with compliant ketchup.
Storage: any leftover potatoes can be kept in an airtight container in the fridge for up to 4 days.