Hi Frank,
Support for HSM keys in Mbed TLS is a work in progress. The way it will work eventually is by plugging an HSM driver under the PSA crypto API, which supports both transparent and opaque keys.
The TLS code can already use the PSA crypto API for some things, including client signature. Enable MBEDTLS_USE_PSA_CRYPTO, call mbedtls_pk_setup_opaque() to create a PK object for the key, and declare the key to the TLS code with mbedtls_ssl_conf_own_cert() as usual.
To create the key, you will need to write a PKCS#11 secure element driver. ("Secure element" = "HSM" for this purpose.) I think it would make sense to have one in Mbed TLS, but I don't know when we might get around to writing one.
There are two secure element driver interfaces in Mbed TLS right now: MBEDTLS_PSA_CRYPTO_SE_C (dynamic secure element interface) and MBEDTLS_PSA_CRYPTO_DRIVERS (unified driver interface). Both are still experimental: we can't guarantee API stability at this stage. MBEDTLS_PSA_CRYPTO_SE_C was the first proposal, and its development is currently frozen and may be abandonned, so I don't recommend investing any effort in it at the moment, but if you need something fast (e.g. for a demo/proof-of-concept), it's your best bet. MBEDTLS_PSA_CRYPTO_DRIVERS is the way of the future, but it's an active work in progress.
If you're creating the key from your application, just call psa_generate_key. If the key was provisioned externally, it's unfortunately not so easy. With MBEDTLS_PSA_CRYPTO_SE_C, you can register a key that's already present in the secure element with mbedtls_psa_register_se_key(). The corresponding facility in the MBEDTLS_PSA_CRYPTO_DRIVERS interface is a "get_builtin_key" entry point, but this is not implemented yet. (There's a prototype at https://github.com/ARMmbed/mbedtls/pull/3822 but nobody is working on it. The specification is in docs/proposed/psa-driver-interface.md.)
There's an example application with a MBEDTLS_PSA_CRYPTO_SE_C driver at https://github.com/ARMmbed/mbed-os-example-atecc608a . We don't have example code for MBEDTLS_PSA_CRYPTO_DRIVERS yet, or good documentation, or an easy-to-use build system — those are still a few months in the future.
If you write a driver in the next few months, I recommend that you stay in touch with the Mbed TLS development team and follow the development branch of Mbed TLS closely, since it's a very active area of development at the moment.