Boil tortellini according to package instructions in a large stock pot.
Add broccoli florets to the boiling pasta during the last 2 minutes, then drain both and set aside.
Heat olive oil in a large skillet over medium-high heat, then cook chicken pieces for 6 to 8 minutes until cooked through and browned.
Remove chicken from skillet and set aside on a plate.
Lower heat to medium and add butter, diced onion, minced garlic, garlic powder, salt, and pepper to the skillet. Sauté for 1 minute until fragrant and soft.
Whisk in flour until fully incorporated with butter and spices.
Slowly pour in chicken broth while whisking constantly to prevent lumps.
Whisk in heavy cream and simmer the sauce for 3 to 5 minutes until thickened.
Stir in 1 cup of the shredded three-cheese blend until melted into the sauce.
Turn off heat and return the chicken, cooked tortellini, and broccoli to the skillet.
Gently stir to coat everything in the creamy sauce.
Garnish with the remaining ½ cup of shredded cheese before serving hot.