Some good ideas for conversation starters with a boyfriend are to ask him to describe a hero and then to ask who his hero is. Another question to follow that is to ask what qualities of those listed he sees in his significant other.
A different idea for starting a conversation is to ask about a time he was touched by the kindness of someone else and how that made him feel. It is also possible to ask the opposite question, looking to learn about a time he was hurt or betrayed by someone, and how that made him feel.
It can also be interesting to ask about his first impression of his partner. This can lead to a discussion about if that impression was accurate or if it has changed over the course of the relationship. Some other questions that lead to conversations about the relationship are to ask about how he likes to be touched and what he considers to be a deal breaker in a relationship.
Another idea for starting a conversation is to ask about values that are important to him, how his family and friends would describe him or when he feels most like himself.
Looking back on his life, it can be interesting to ask about a favorite childhood book or movie, or to ask what he wanted to be when he grew up.