Preheat the oven to 400 degrees. In a large braiser or skillet (you will need a lot of room for all the vegetables), cook the sausage over medium heat until browned. Remove the sausage from the pan and place into a separate bowl. Pour off the excess grease (don’t bother cleaning it as this will help flavor the hash).

Add the 3 tablespoons of oil to the same pan over medium heat. Add in the sweet potato cubes and onion slices. Stir to coat the vegetables in oil and sprinkle with 1/2 teaspoon of kosher salt. Cook for 5 minutes so the potatoes and onions just start to soften, stirring occasionally. Next, carefully stir in the broccoli and minced garlic. Sprinkle with 1/2 teaspoon black pepper and an additional 1/4 teaspoon of salt and stir. Cook for an additional 3 minutes. Add the cooked sausage, stirring one more time to evenly distribute the ingredients.

Turn off the heat on the stove and transfer the hash to the preheated oven. Bake for 20 minutes. Remove from the oven and use a spoon to make four small “pockets” in the hash. Carefully crack eggs into each pocket. Sprinkle each egg with additional salt and pepper, if desired, and return to the 400 degree oven. Bake for an additional 8-9 minutes, or until eggs are just set.***