Bring 2-1/2 quarts of unsalted water to a boil in a covered 4-1/2-quart or larger Dutch oven or soup pot. When the water reaches a rapid boil, add the bow ties and cook until tender, 9 minutes.

Meanwhile, if the chicken breasts are frozen, run them under hot water so you can remove any packaging. Place the chicken on a microwave-safe plate and microwave 3 minutes, uncovered, on high, to begin defrosting. While the chicken defrosts, melt the butter on medium-low in a 12-inch nonstick skillet. Peel and chop the onion, adding it to the skillet as you chop. Cook until the onion is soft, about 3 minutes.

Slice the chicken (fresh or partially defrosted) into 1/2-inch strips. Raise the heat to medium-high and add the chicken. Cook until the chicken is no longer pink in the center, 3-1/2 to 4 minutes, stirring often. Meanwhile, place the broccoli in a microwave-safe dish and microwave 3-1/2 to 4-1/2 minutes, covered, on high, until it is just warm.

Remove the chicken from the skillet with a slotted spoon and set aside. Reduce the heat to medium-low. Stir the sour cream and half-and-half into the chicken juices to blend well, then add the mustard, Worcestershire, and garlic powder. Stir well and continue to cook until the sauce is slightly thick, about 2 minutes. Do not boil.

Return the chicken to the skillet and add the broccoli, then raise the heat to medium-high and bring the sauce almost to a boil. Reduce the heat to low and simmer to blend the flavors, 1 to 2 minutes. Do not boil.

Meanwhile, drain the bow ties and place some on each serving plate. Top with the chicken mixture and serve.