Boil pasta according to package directions. Once pasta is finished cooking and right before draining, add broccoli, stuffing down into water. Remove from heat and let sit for 1 minute or so before draining. Set aside.
Meanwhile, while pasta is cooking, heat olive oil in large skillet over med-high heat. Add chicken and saute for 4-5 min until browned. Remove chicken from pan and wipe clean.
Add butter and let melt over med-high heat. Add garlic and saute for 30 seconds. Add flour, and whisk. Add milk 1/2 cup at a time, whisking to combine. Sauce will start to thicken. Add chicken broth after you're finished adding milk. Continue whisking. Add cream, salt and pepper, nutmeg and parmesan cheese. Whisk to combine.
Add chicken back into skillet, along with cooked rotini and broccoli. Toss to combine. Add red pepper and stir well. Cook for another 4-5 min until all veggies are softened.
Garnish bowls of pasta with red chili flakes, pepper, freshly grated parmesan and fresh basil if desired. Serve and enjoy!