Heat a large skillet over medium heat and add 2 tablespoons of the olive oil.
Add the diced onion and sauté until softened, about 3–4 minutes.
Season the bite-sized chicken pieces with the kosher salt and freshly ground pepper.
Increase heat to medium-high, add the chicken to the skillet, and brown the pieces, about 4–5 minutes.
Add the minced garlic to the pan and cook for about 1 minute until fragrant.
Push the chicken and onions to one side, add the remaining 1 tablespoon olive oil to the empty side, then add the uncooked rice and sauté for 2 minutes to coat and lightly toast.
Pour in the chicken broth, stir to combine, bring to a boil, then reduce heat to a simmer and cover with a lid.
Cook covered for about 12 minutes.
Uncover, add the broccoli florets, stir to combine, then recover and continue cooking on low for about 8 more minutes, until the rice and broccoli are tender.
Remove the skillet from the heat and stir in 1/2 cup of the shredded cheddar until combined.
Sprinkle the remaining cheese over the top, cover, and let sit 1–2 minutes until the cheese melts, then serve.
