Ahah! I see what you did there.
- Dig away a single block of the cliff to give yourself a place to start. You can be pretty tricky and do this a very long distance from your proposed cavern so it isn’t too obvious. The level of the block you dig out is going to be the same as the floor/roof you want to dig through.
- Dig the entry tunnel into the area you want to make a cavern in.
- Go into x-ray mode to designate a strip at the level of the roof over the tunnel to the room. Designate a second strip one tile higher as well.
- Build at least one ladder for the hearthlings to reach the roof with. They will now tap away at the pieces of roof they can reach until you have a small hole going up.
- Remove the mining zones you’ve made so far. They have done their job.
- Use x-ray mode and the 4x4x4 mining tool. Select the very top of the area you’ve already dug out. You may need to extend your ladders so the hearthlings can get up far enough, but they’ll dig their way up into the next slice.
- Repeat steps 1-6 until you’ve dug far enough upward.
- Dig sideways at the top level until the room is wide and long enough.
- Dig down from the top. Don’t forget to remove the ladders as you go. They won’t dig out the blocks under the ladders until you do.
Note: Using the mining tool in x-ray mode is a bit glitchy as you can’t actually see the mining zone after you’ve released the cursor to set it. Sometimes you have to switch back and forth between modes and heights to get into a slice mode where you can see the mining zone in the roof and remove it after it’s done its job. I’m sure @Albert knows all about this since he figured out the essential trick first, but I’m just putting this out there for anyone else.