Textbooks! Good textbooks strike a balance between coverage, depth and compression of reasonably current knowledge. They're not cheap brand new, so consider buying $current_ed-1.
When I want to learn a topic, I literally buy a textbook and plow through it. Sometimes I'll buy a handbook or student's guide or pop. account of the subject to go alongside.
I took an accounting unit at university. One of the smartest decisions I've ever made. I even crack the book from time to time to refresh my memory about something.
Start with a financial accounting book intended for freshmen students in your country, and then management accounting (which is largely universal), and branch from there. A lot of accounting is actually about adjusting for imprecision; meanwhile, finance is about uncertainty.
There's even a software-focused management accounting / finance book: Return on Software by Steve Tockey[1]. It's good.
When you have the basics of this stuff, lots of business chatter becomes much more comprehensible. Your clients will appreciate that you speak their language and understand their pain points (cashflow is the biggest pain in any small business).
TBH I would recommend not doing any textbook learning. This aplies to most enterprises, not just finance, but your 'domain expertise' comes from work experience in that domain. Hence the obvious chicken/egg problems, so the best way to crack it is to hustle your way into getting ANY contract in that domain. You may have to exaggerate, do 'boring' work, undercut, whatever, but once you got 1 contract under your belt, then you can position yourself for the more desirable ones.
I have to ask if actually want to work in finance, or just want more money. If it's the latter, then all you may need to do is sell yourself better (see my other comment); the rates in finance are not what they used to be, and unless it's a highly specialised skill, pretty much most enterprises pay the same range for similar roles.
If you actually want to work in a deep speciality in finance (which also are the most interesting roles), then get a contact close to that target, and then hustle your way in. In both cases you still need to sell yourself.
Also, if your not in a major financial center, then move.
Forgot to mention that the specialised learning will naturally happen on the job, when your speaking daily with the experts. Though a bit of wikipedia learning can't do you wrong just to talk around the subject.
I'll hunt those textbooks and try to find it, but "domain expert in finance" sounds cryptic.
What's the actual job title for the $400+/h job?
Oh, I once got an invite by McKinsey, but I declined the job offer. I believed that they won't support me learning more skills and that I can earn more as Software-Engineer. I don't know I was wrong now.
And I'm still pretty underpaid, ranking in the low mids.