In a large skillet or pan, combine oniions in two tablespoons of olive oil over medium heat
Add chicken, brown, then add garlic. Cook for an additional minute
Push chicken to one side of pan and add 1 tablespoon extra virgin olive oil.
Add uncooked rice, saute for a few minutes
Add chicken broth and boil.
Cook chicken and rice covered for 12 minutes.
Sprinkle broccoli evenly over chicken and rice mixture, stir
Continue to cook until broccoli and rice are tender, 7-10 minutes
Remove from heat, sprinkle in half a cup of cheese
Top with remaining cheese, let sit till melted.
Serve!