That’s not how public key cryptography works.

You don’t go and buy an SSL certificate from a CA. You pay for them to /sign/ your public key, presumably after verifying your identity. You generate the public/private key pair, and then you keep the private key private.

The CA could in theory sign Eve's private key along with metadata saying that private key belongs to you, but that just gives someone the ability to impersonate you. It doesn’t give Eve the ability to read emails that Bob sent to you with a key wrapped with your public key.