Bring a small pot of water to a boil, carefully lower in the eggs, and simmer for 6.5 minutes.
Immediately transfer the eggs to an ice bath for 5 minutes before peeling and halving.
While eggs cook, cut the Brussels sprouts in half and dice the chicken breast into bite-sized pieces.
Heat olive oil in a large skillet over medium-high heat and add the chicken, seasoning with half the salt, pepper, and garlic powder.
Cook chicken for 5-6 minutes until browned and cooked through, then remove from the pan and set aside.
In the same skillet, place Brussels sprouts cut-side down and sear for 4-5 minutes until deeply caramelized and tender.
Return the chicken to the pan, add the remaining seasonings and apple cider vinegar, and toss to combine.
Plate the sprout and chicken hash and top with the jammy egg halves.