The key thing with a good mushroom is keeping a rim of bark. Not all types of tree can do this and even those that can will only do so if the tree was cut down in the winter. The sugary sap just under the bark in summer decomposes and it comes off however careful you are.
The other key thing is undercutting the bark rim to get the edge to undulate with the tree’s natural deviation from truly round. The skill is doing it without lifting the bark off.
This one is in Ash which is close to round.