How to extract equity from turning basement into rental unit on paid-for house?

[Nate McCarthy]

My mom lives in a nice house that she has paid off. However to save money when she had the house built, she left the basement unfinished--it is just studs, insulation, and windows/doors, plus plumbing in the foundation. There's obviously opportunity here to build this out and turn it into a basement apartment, which I think would cash flow because of course there's no mortgage. 

What I'm wondering is: is there a way to get the cash invested into this rehab back out of the property in a relatively short timeline, as if it were a BRRRR? If I had just bought this property and could force some appreciation, I could refinance and hopefully extract that equity within a year, for example--but since this house is paid off, refinancing would introduce a new mortgage payment.

What are the options here? Get a new loan only for the equity created by this rehab? Refinance the whole house as long as the rent exceeds the mortgage? Just let the money live in the house and collect rent as the only ROI?

Thanks for the insight!