In a 12" non-stick skillet, drop in 1 Tablespoon of butter. Place on medium-high heat until melted.
Add chopped onions and cook until slightly softened, stirring frequently.
Add chicken. Turn often till chicken is just starting to brown.
Reduce heat to medium. Add another tablespoon of butter to the edges of the skillet, melt.
Pour uncooked rice around the perimeter of the pan, with the chicken in the center.
Sautee the rice in the butter to coat the grains.
Make a hole in the center of the chicken, in the center of the skillet and add the garlic.
Cook the garlic for 30 seconds.
Pour in the chicken broth and the vermouth. Heat until boiling.
Turn heat to low. Cover skillet with a lid and cook for 12 minutes.
Carefully open the lid. Add last tablespoon of butter and paprika. Stir contents. Sprinkle chopped broccoli on top of everything. Return lid and cook another 8 minutes.
Carefully lift the lid and gently stir the mixture. Remove from the heat.
Sprinkle cheese on top of everything. Return the lid and allow to sit for about two minutes.
Top with parsley and serve.