Back to Hollow Knight
The White Palace can be found by Dream Nailing the Knight in the Palace Grounds of the Abyss. It’s a difficult platforming section that will be sure to make you rage unless you’re very patient. There are three main sections with Benches in between each one. For each section you’ll need to find the lever to access the lift to the next section.
Once you make it to the very top of the palace you’ll find a dead King sitting on a throne. Hit him a few times to knock out half of the Kingsoul charm.
Due to the difficulty of this area and the fact that you’ll only take one damage at a time it’s highly recommended to equip the Hiveblood charm to regenerate your health.
Once you have both halves of the Kingsoul equip this charm at a Bench. Head down to the bottom of the Abyss and wait for the ground to fall away, revealing a passage down to the Birthplace. There’s not too much to explore down here as I think this area was reserved for future development. If you explore all of the passages you’ll find an Ancient Egg, and then a large black egg. Use the Dream Nail on the egg to be taken back to the bottom of the Abyss. Jump your way back up to the top of the Abyss to see another Hollow Knight. After the cut-scene you’ll be given the Void Heart charm.