Prep the ingredients per the instructions above.

Preheat the oven to 400°F (204°C).

Prep the potatoes: Cut the potatoes into ¼inch-thick sticks. Place into a large bowl and cover completely with cold water for 20 minutes (see note). Drain well and pat dry with a towel. Place on a foil-lined baking sheet. Cook in the oven, tossing halfway through until golden brown and crispy.

For the gravy: Heat the butter in a saucepan over medium heat. Brown the sausage, breaking it up into smaller pieces as it cooks. Stir in the flour and cook while stirring for 1 minute. Whisk in the milk and parsley; bring to a simmer until it starts to become thick and smooth. Season with salt and pepper to taste. Cover with a lid and set aside.

Preheat the broiler over low heat.

Arrange the fries onto a parchment-lined baking sheet. Pour the sausage gravy over the fries. Top with cheese. Place under the broiler until melted.

Make the eggs: Heat the butter in a nonstick pan over medium heat. Crack the eggs into the pan and cook until the white is set. Set aside.