After cooking the corned beef, pour the pan drippings into a bowl. You'll need about 3 tablespoons of drippings for the gravy. If you don't have enough drippings, you can top it up with butter to make up the difference.
In a saucepan, heat the 3 tablespoons of pan drippings over medium heat. Once the drippings are hot, add the 3 tablespoons of flour to the pan. Stir continuously with a whisk or wooden spoon until the flour is fully incorporated and the mixture becomes a smooth paste, known as a roux.
Continue to cook the roux for 1-2 minutes, stirring constantly, to cook off the raw flour taste. Be careful not to let it burn.
Gradually pour in the 500 ml (2 cups) of beef broth or beef stock, stirring constantly to prevent lumps from forming.
Add a pinch of salt and a pinch of pepper to the gravy, adjusting the seasoning to taste.
Bring the gravy to a simmer over medium heat, stirring frequently. Allow it to simmer for 5-10 minutes, or until it reaches your desired thickness. If the gravy is too thick, you can add more beef broth to thin it out. If it's too thin, you can let it simmer for longer to reduce and thicken.
Once the gravy reaches the desired consistency and flavor, remove it from the heat. Serve it hot over your corned beef hash and fried eggs.