Preheat oven to 350°F. Grease a 13x9” baking dish, set aside.
In a large stock pot to 8 cups boiling, salted water add the broccoli and blanch for 2 minutes. Remove and set aside. Cook pasta per package instructions, set aside, reserving 1/4 cup of pasta water.
Rinse and pat the chicken dry with paper towel. Cut into 1-inch pieces if using breast meat or leave in strips. Toss with salt, pepper and 2 tablespoons of flour to coat.
In same pot over medium-high heat add 2 tablespoons oil and sauté the chicken. Turn to brown on all sides. Add more oil if needed. Transfer to a platter and keep warm. Chop strips if needed.
Add remaining oil and sprinkle in remaining tablespoon of flour. Cook on medium for 2 minutes. Whisk in the chicken stock and deglaze the pan by scrapping up bits of browned food on bottom of pan and bring to a boil. Add the reserved pasta water, milk and whisk in cheese. Whisk in the mustard and tarragon, return to simmer and cook for 2 minutes.
In prepared baking dish add the chopped chicken, tortellini, broccoli and toss to mix together. Pour sauce over all, cover with aluminum foil and bake for 15 minutes until everything is warmed through and bubbling.