i don't think laravel has to do anything with TLS. It must me your web server (apache or nginx). Configure your webserver to support TLS 1.2
For apache you can look this answer
https://serverfault.com/questions/314858/how-to-enable-tls-1-1-and-1-2-with-openssl-and-apache
For Nginx you can look this
https://askubuntu.com/questions/319192/how-to-enable-tls-1-2-in-nginx
You might be using Guzzle with TSL 1.0, configure it to support 1.2. here is the link
How do we specify TLS/SSL options in Guzzle?
To Support mysql to use TLS 1.2 configure it like this in my.cnf
[mysqld]
tls_version=TLSv1.1,TLSv1.2
For details check here https://dev.mysql.com/doc/refman/5.7/en/encrypted-connection-protocols-ciphers.html
Note: Prior to MySQL 5.7.10, MySQL supports only TLSv1, for both
OpenSSL and yaSSL, and no system variable or client option exist for
specifying which TLS protocols to permit.