The same appearance and properties that the burrows already have in the game.
The above-ground part of the burrow can be built from couple of branches, boughs and soil, and then we can dig up tons of soil to create the underground space (similar to building a basement).
If we dig without a shovel then we get the smallest room, with wooden and tinker's showel we get the medium size room, and with metal shovel we get the largest room.
I guess it's easy to implement since all these objects already exist in the game.
Here's another more complicated but interesting suggestion from Papermoon in discord channel:
1. Can be built as a cheap house alternative. Made the same way cellars are made where you have to dig out the dirt until you can enter
2. Can mine/dig walls inside to extend burrows to max dimensions by digging walls with no risk of cave-in which can act like a mining tutorial.
3. Can lock burrows like a house so that a crime is needed to enter. Maybe by putting up a circular door hobbit style
4. Can build more inside of burrows such as drying racks and campfires to make it more useful early game (same options as cave tiles?)
https://discord.com/channels/1194708350491963565/1318384387322282065/1318384387322282065