Note: I am fully Aware 1 Mushroom wall works, but as said further down, I combined mine with getting the pet achieve as well.
The mushroom pet house counts for this.
You will need 2 items to create this
The oven and the grinder.
The grinder can be bought from BURG.L after getting the haze lab chip and buying the Advanced Production Buildings after returning to BURG.L
The Oven needs;
10 Clay (near large bodies of water)
1 Charcoal Chunk (near the barbecue at the pond)
4 Boiling Gland (from Bombadier Beetles)
The grinder needs
2 Crow Feather Piece
2 Acorn Shell
3 Flower Petal
5 Bombardier Part
Once you have these, you need to turn the new mushrooms into slurry using the grinder then cook them in the oven, you will need to then take the brink to be analysed. This will unlock the pet house, you will need the following items to make the house,
2 Weed Stem
1 Acorn Shell
4 Mushroom Brick
2 Crow Feather Piece