Work on the spreading

It's not natural.

Thank you.
What do you mean by exactly? Is the grammar point is incorrect or the general pattern of speaking in this kind of situation?

If you worked in a catering establishment and had to spread peanut butter on a couple of hundred slices of bread, you might say that you were going to work on the spreading. It's inappropriate if you are going to spread the butter on one slice.

Thank you.

then if I said, work on some spreading, would it have been ok?

No.

Thank you.

How about this way?:

When I am finished with this piece, I will do the spreading" (spreading butter on another piece)

Can someone give me an answer for this?

No, don't talk about "doing the spreading" unless (as 5jj has already said) you are doing something like making 500 peanut butter and jelly sandwiches for a caterer.

I will spread peanut butter on another slice of bread.

It's still awkward English. If you really want to say it, you have to include words that tell us you are talking about another piece.
eg When I am finished with this piece, I will do the spreading on another one. Sounds poor
eg When I am finished with this piece, I will spread another one.

Thank you.

The thing I can't get is that why this ing form is denoting such repeated action.

You say I need to do some washing for just one time work with your washing machine, and let's work on painting/coloring for just an art project or simple coloring, but why this spreading is carrying so much more than what appears to be?