In a large skillet, heat the olive oil over medium-high heat.
Add the shallot and cook until it starts to soften, about 3 minutes.
Add the garlic and cook another minute.
Add the chicken breast pieces and cook until browned, about 5-7 minutes. It does not need to be cooked through.
Add the rice, chicken broth and milk; stir well to combine. Season with salt and pepper.
Bring to a simmer, reduce heat and cover with a lid. Let simmer for 10 minutes, stirring every couple of minutes.
Remove the lid, add the broccoli to the mixture, cover and cook another 5 minutes, or until liquid is absorbed and broccoli is softened.
Stir in 1 cup of cheddar cheese, then sprinkle the remaining ½ cup on top. Cover and let the cheese melt for 1-2 more minutes. Serve and enjoy!