Add chicken broth and rice to a medium-sized saucepan then turn heat to high to bring to a simmer. Turn heat down to low then place a lid on top and simmer for 6 minutes (rice should barely be simmering so make sure the heat is not too high.)
Add broccoli (no need to stir) then place the lid back on top, turn heat up to keep broth at a gentle simmer, and then cook for an additional 9-10 more minutes or until the rice and broccoli are cooked through. Turn off heat then sprinkle in cheese and stir until completely melted. Stir in ham until warmed through, then serve.