The Will O' the Wisps lead Princess Merida to her hut, where the woman there insists in presenting herself as a simple wood carver. But Merida rapidly realizes her real nature after seeing a broom moving by itself, a speaking crow, and other abnormal wonders. The witch tells her that she's not a witch due to too many unsatisfied customers and tries get rid of Merida with floating knives until Merida offers to buy all of her carvings. In exchange of buying her entire stock, Merida convinces the witch to give her a spell in the form of a cake, to change her mother. Just as Merida leaves with the cake, the witch realizes she forgot something very critical about the spell, but is too late to tell Merida.
When Merida comes back to the witch's hut, hoping to find a remedy to the spell, she instead finds that the witch is gone and left a potion-powered automated message that says she left for the Wicker Men Festival in Stornoway and won't be back until spring. She reveals that she forgot to mention to Merida that the spell will become permanent by the second sunrise. The witch also reveals a cryptic riddle to Merida: "Fate be changed, look inside, mend the bond torn by pride," which was the answer to reverting the spell. After the witch repeated the riddle, she disappeared. Merida, not yet understanding the riddle, pours the other message potions into the cauldron, but it only ends up blowing up the cottage. As it starts to rain, Merida uses the pieces of what's left of the cottage to make a shelter for her and her mother.
The Pizza Planet truck from Toy Story in Brave (seen here in front of the witch)
Sulley on a piece of wood, visible in the bottom right corner of this image
A113 appears as ACXIII above the door
A carved portrait of Joe Ranft appears on the side of this small wooden box
The reference to Newt in Brave
The Luxo Ball in Brave
Merida and Belle in the cottage in Once Upon a Time
Various Pixar Easter eggs can be seen inside the Witch's Cottage; in fact, all Easter eggs are found inside the cottage itself: