That is exactly how the handle on my two gallon ice cream machine was attached.
Mine is not a White Mountain but it works just like one and was made in India.
It was so easy to take my handle off because when I opened the box the handle was not attached.
The funny thing was the threads were 1/2-12tpi
Them folks in India must have copied an old freezer too closely
I ordered a tap & die and since the pulley I was going to use had a 1" bore I center drilled a piece of 1" rod, tapped it then cut it off about 1 1/4" long to make a bushing for the pulley.