Heat the olive oil in a medium sauce pan over medium heat.
Add the rice and stir to coat. Toast the rice, stirring often, just until it starts to turn golden.
Pour in the chicken broth, bring to a boil, turn heat to low, and cover.
Cook, covered, for 10 minutes.
While the rice is cooking, chop the broccoli into small, bite-sized pieces.
After 10 minutes, add the broccoli and ham to the pot with the rice and cover again. Continue cooking for 5 minutes.
Turn off the heat and let set for 10 minutes without removing the lid.
Remove the lid, fluff the rice with a fork, and add the butter, cheddar, and garlic powder. Stir until well incorporated. Cover and let sit for 5 minutes more.
Stir again and add salt and pepper to taste and a splash of milk if you'd like to thin out the mixture a little bit, if needed.