How do I search "Recents" in the Phone app?

John,

There is no UI to search "Recents." As you already know, you have to scroll through the list, which contains up to 100 of your recent calls.

You can make your need known by submitting iPhone Feedback.

There is no way to do this IMO. I checked myself and I could not find a way, sorry.

Most carriers keep a call log if you are needing to see a longer record of your calls. It would be worth contacting your carrier for a means to retrieve such a list, if this was your intent.