Heat olive oil in a large skillet over medium-high heat.
Season the chicken pieces with kosher salt and black pepper.
Add the chicken to the skillet and cook for 5-6 minutes, stirring occasionally, until browned and cooked through. Remove chicken from skillet and set aside.
In the same skillet, add the chopped onion and cook for 2-3 minutes until softened.
Add the minced garlic and cook for 30 seconds until fragrant.
Add the broccoli florets and cook for 3-4 minutes until bright green and slightly tender.
In a bowl, whisk together the heavy cream, chicken broth, Dijon mustard, and paprika.
Pour the cream mixture into the skillet with the broccoli and onions. Stir and bring to a simmer.
Return the cooked chicken to the skillet and stir to combine.
Sprinkle the shredded cheddar, mozzarella, and Parmesan cheeses evenly over the top.
Cover the skillet with a lid and cook for 5-7 minutes over low heat until the cheese is melted and bubbly.
Remove from heat and let sit for 2 minutes before serving.