"Have" is the helping verb and the main verb. It's in the Past Perfect tense, so it's "had had." The adverb "just" is placed between the helping verb and the main verb, so we end up with "had just had." "Just had" would be the Simple Past tense, but the Past Perfect tense gives us more specific time information. It tells us that the conversation had happened before the moment she had the thought.

It's because she HAD a conversation. If she had SUNG a song instead, you would say "She recalled the song she had just sung with the young woman". Replace "song" with "conversation" and replace "sung" with "had" and you will be having a conversation instead of singing a song.