This will print BranchName - CommitMessage - Date as (YYYY-MM-DD). You can manipulate/edit this command line to suit your need.
git for-each-ref --sort=committerdate refs/heads/ --format='%(HEAD) %(color:yellow)%(refname:short)%(color:reset) - %(contents:subject) - %(authorname) (%(color:green)%(committerdate:short)%(color:reset))'
Note that it will print for all local branches, not just current branch. You can create an alias for convenience.
[alias]
branchcommits = !git for-each-ref --sort=committerdate refs/heads/ --format='%(HEAD) %(color:yellow)%(refname:short)%(color:reset) - %(contents:subject) - %(authorname) (%(color:green)%(committerdate:short)%(color:reset))'
and run git branchcommits in git bash prompt.