Bring a large pot of salted water to boil. Cook pasta according to package directions. Reserve 1/4 cup pasta water before draining. Add broccoli florets during the last 3 minutes of pasta cooking time. Drain pasta and broccoli together and set aside.
Heat olive oil in a 12-inch skillet over medium heat. Add minced garlic and cook for 30 seconds until fragrant, stirring constantly to prevent burning.
Add shredded rotisserie chicken to the skillet. Stir and heat through for about 2 minutes until warm.
Stir in chicken broth, Greek yogurt, and Parmesan cheese. Whisk to combine and simmer for 2-3 minutes until sauce thickens slightly. Add reserved pasta water if sauce is too thick.
Add cooked pasta and broccoli to the skillet. Toss everything together using tongs until evenly coated and creamy.
Season with dried oregano, red pepper flakes if using, salt, and black pepper to taste. Toss once more and remove from heat.
Serve immediately while hot, garnished with extra Parmesan cheese and fresh parsley if desired.
Notes
Use any pasta shape you prefer. Whole wheat adds extra fiber and protein, but regular, chickpea, or gluten-free pasta work too.
For a creamier sauce, increase Greek yogurt to 1/3 cup. Full-fat Greek yogurt creates the richest texture.
If sauce is too thick, add reserved pasta water one tablespoon at a time. If too thin, simmer uncovered for 1-2 more minutes.
Don’t have rotisserie chicken? Use any cooked chicken breast or thighs.
A 12-inch skillet is recommended to comfortably fit all ingredients.