Maybe this is a phrase in the US, but in Br.English you say " I will make soup" or "I will prepare soup". One of those oddities of language!
Same in the US. We definitely do not cook out soups haha.
Θα φτιάξω σούπα.
And "μια" is completely unnecessary.
"I will cook up a soup." - is a common expression in English.
Would you accept this as an alternative translation?
So it is but we can't be adding all possible expressions. Your contribution is appreciated so please send more.