Have you looked at the documentation or are you just guessing? When you realize how impenetrable OpenSSL or any TLS lib documentation looks to people untrained in cryptography, you would gain a new appreciation for Git man pages!
Between the docs[1][2] and the examples[3] I was up and running using my own IO stack in a couple of evenings. If I had used the IO stack from the library it would have been very easy.
Another couple of evenings and I had it integrated with Windows' certificate store. In the end it wasn't very difficult to implement, but it was a bit more of a challenge figuring out the documentation and how it related to mbedTLS.
Definitely a rewarding experience, gave me some nice insights into the plumbing.
edit: Note, not trying to argue replacing libcurl is a weekend project!
[1]: https://mbed-tls.readthedocs.io/projects/api/en/latest/
[2]: https://mbed-tls.readthedocs.io/projects/api/en/latest/api/g...
[3]: https://github.com/Mbed-TLS/mbedtls/blob/development/program...