Cook the Potatoes - Heat butter and olive oil in a large 12" cast iron skillet or pan over medium-high heat. Once melted, add the potatoes, salt, and pepper, and stir to combine. Cook, stirring occasionally, until the potatoes are golden brown and tender but not fully cooked, about 6 to 8 minutes. Reduce the heat as needed to prevent burning.
Saute the Aromatics - Reduce the heat to medium. Add the onions and saute until translucent, about 3 minutes. Add the garlic and saute until fragrant, 30 seconds.
Brown the Beef - Add the corned beef, and stir to combine. Spread in an even layer, lightly press down, and cook undisturbed until the surface is browned, 1 to 2 minutes. Stir and spread, cooking for another 2 to 3 minutes, until the potatoes are fork-tender.
Serve - Garnish with parsley, then transfer to plates. If desired, serve with eggs, hot sauce, or Worcestershire sauce, and toast.
Notes
Storing: Refrigerate in an airtight container for up to 3 days.
Reheating: Cover and microwave on high setting in 15 to 30 second increments until hot. Alternatively, reheat on the stovetop over medium-low heat until hot.
Using Canned Corned Beef - Use two 12-ounce cans. Make a well in the center of the pan and break it into smaller chunks. Stir and spread into an even layer. Cook for a few minutes until browned, then flip and cook the other side until browned.