What happens if you Brush a Brush? Can you swap back the original battlefield you Brushed?

The Brush token will cease to exist. When swapping back, a player can choose to swap back to any object that was replaced, including the original battlefield.

This is because a replacing game object inherits all of the statuses and conditions of the game object it replaced, per 438.1. A game object can be instructed to “swap back”; the token stops existing and the original card is returned to the space that the token occupied, inheriting all its current effects and statuses per rule 438.7.b. “All of the effects and statuses” includes not only temporary effects applied to the battlefield, but also the relationship between replaced and replacing battlefields.

Rule 438.1.: Replacing is the act of Creating a token in the place of another card or token without playing it while inheriting all effects or statuses of the game object it replaced. Rule 438.7.b.: To Swap Back, the token stops existing and the original card is returned to the space that the token just occupied, inheriting all current effects and statuses.