A mug or small bowl that a puck fits in snugly should be able to nest inside a slightly larger dedicated lathering bowl when not in use. That should save a lot of real estate.I'm going to move the soap puck into a separate bowl and go back to properly warming/soaking my brush for my next shave. My wife won't be happy with the additional bathroom counter real-estate I take up, but I'm pretty confident this will pretty drastically improve my lather.
Many of us made our lather on top of a cake of soap in a tallish mug in the old days but I think it's easier to load the brush from the container that holds the soap or cream and move to a separate bowl to build your lather. You use a bit less and have more room to work up your lather.
Other posters, like the guy above, will tell you to face lather. Try that too. Personally, I don't care for it.
You can load your brush in your soap bowl then take it to your face to build your lather (called face lathering). IF you take your loaded brush to another bowl and whip a later to "paint" on your face this is bowl lathering.
Go over the lathering info in the shave wiki for more details:
I need a good metal lathering bowl, I keep breaking my glass/ceramic ones
I do that with bowls and large mugs, in the sink with not quite enough water for them to float.Before I got a scuttle, I submerged a coffee cup in the sink of hot water to warm my lather.
Search on eBay for "copper shaving bowl". The $7 ones are as good as the $12 ones. They come in several sizes, so make sure you are getting one the size you want.
If you drop it on the counter you can usually push the dent out with your fingers.
turkish copper hammered bowl, about $15 on Ebay. makes a great lather.I need a good metal lathering bowl, I keep breaking my glass/ceramic ones