There are a few ways to interpret the concept of simultaneously expressing a basic belief and showing evidence for it in a consistent way. Interpreting the statement non-literally is a cop-out, but it is a way to interpret it.
Let's take the concept of a basic belief at face value for a moment. There are a few things you can do that are internally consistent.
One thing that you can do is to argue that a particular explanation in language is a good description for a basic belief that someone else already has.
You can also argue that someone else should accept a belief that is properly basic for you but would merely be inferential/derived/non-basic for them.
We can also take the concept of being a "basic belief" not at face value and interpret it instead as a commentary on what constitutes evidence for a belief and how beliefs work in general.
Finally, I don't think there's a requirement that some collection of basic beliefs be minimal. I can articulate a "redundant" set of five basic beliefs, but some of them are "theorems" of other beliefs. I don't say which of them are foundational because they're all foundational. Nevertheless I might end up concluding the same things if I took one of those beliefs and de-basicked it. If my collection of basic beliefs is non-minimal, then I would expect some of the basic beliefs to be provable using other ones.