The broad hatchet, or side axe, is a scaled down version of the broad axe. I use my broad hatchet all the time to quickly rough out the shape I’m trying to form. You can remove a lot of wood with moderate precision. A regular hatchet is double beveled whereas a broad hatchet is single beveled. The bevel is most commonly on the right side for right handed users (flat side up against the work). There are situations where it makes sense to have the bevel on the left (bevel side up against the work). With the bevel against the work you can carve out concave shapes. The bevel of the blade forces the blade back to the surface, much like a using a chisel bevel down.
You’ll want a broad hatchet with a handle that you can grip in two places, at the bottom for taking big swings and at the top for delicate work. Some people prefer to choke up on the handle and extend a finger along the beveled side for better control.
If you’re removing a large amount of wood you may want to borrow the hewing technique of scoring. Score the work by cutting deep 45 degree cuts along the length of your work, then come back through and shave the chunks off, removing the bulk of the wood.