Well the usual way is to first create a signed JWS and get the compact representation, and then to encrypt this payload as a JWE.

First create the keys:

signing_key = JOSE.JWK.generate_key({:ec, :secp256r1})
encryption_key_private = JOSE.JWK.generate_key({:rsa, 4096})
encryption_key_public = JOSE.JWK.to_public(encryption_key_private)

Of course, when encrypting, you won’t have the encryption private key.

Sign the payload and then encrypt it:

signed_payload = JOSE.JWS.sign(signing_key, "some message", %{ "alg" => "ES256" }) |> JOSE.JWS.compact |> elem(1)
encrypted_payload = JOSE.JWE.block_encrypt(encryption_key_public, signed_payload, %{ "alg" => "RSA-OAEP", "enc" => "A256GCM" }) |> JOSE.JWE.compact |> elem(1)

Finally you can decrypt and check the signature:

decrypted_payload = JOSE.JWE.block_decrypt(encryption_key_private, encrypted_payload) |> elem(0)
JOSE.JWS.verify(signing_key, decrypted_payload) |> elem(0)

Verification usually involves checking the recipient and the sender of the token, otherwise you can have some subtle but problematic security issues. See https://crypto.stackexchange.com/questions/5458/should-we-sign-then-encrypt-or-encrypt-then-sign and the first link of the first response. Again, rolling out your own crypto is dangerous if this is what you intend to do.