What is the recommended way to break into a phone contact?

The standard and most polite way to join an ongoing voice (phone) conversation is to simply state your call sign once during the pause between the other stations' transmissions. This quickly identifies you to the current operators without severely disrupting their contact. If the operators want to let you in, they will acknowledge your call sign. Using CB radio slang like "Breaker Breaker" is strongly discouraged in amateur radio and is considered poor operating practice. Additionally, saying "QRZ" is incorrect because it is a Q-signal meaning "Who is calling me?", and "CQ" is exclusively used to solicit a brand-new contact on a clear frequency, not to interrupt an active one.