To a large, 12-inch cast-iron skillet over medium-high heat, add chopped bacon.
Cook bacon until crispy, 14-16 minutes, and remove from pan.
Add onion, garlic, and rosemary to the skillet. Cook until they begin to brown, stirring occasionally. Reduce heat to medium.
To a large bowl, add the thawed hash browns, salt, and pepper. Spread the potatoes in the skillet in an even layer. Cook undisturbed for 3-4 minutes, or until slightly crisp.
After cooking the potatoes, add the olive oil to the skillet.
Add in Brussels sprouts and bacon. Stir and gently press into the pan. Leave undisturbed for about 3 minutes. After 3 minutes, flip and stir again. Let cook undisturbed for another 3 minutes. Repeat about 5 times (15-18 minutes of cooking), or until to your desired crispness.
Meanwhile, in a medium saucepan, bring 2 inches of water and the vinegar to a boil.
Reduce to a gentle simmer and stir the water. (The circular motion helps to bring the egg and yolk together.)
Break an egg into a small bowl, submerge the bowl's lip in the water, and slide in the egg. Cook for 2-3 minutes, or until the egg reaches your desired consistency.
Transfer the egg to a paper towel to drain excess water.
Repeat with the two remaining eggs.
Serve the eggs over the hash.