Melt the butter and olive oil in a large skillet.  Slice the chicken breasts to about 1/2" thick and place them in the pan.  Sprinkle with salt, onion powder, garlic powder, and basil.

Cook the chicken for 5 - 8 minutes on each side until browned and cooked through.  Meanwhile, boil the pasta's water and steam the broccoli in a pot.

Remove the chicken from the pan.  Start the broccoli steaming and get the pasta into the (hopefully) boiling water.  Add the garlic to the skillet you cooked the chicken in and saute for 2 - 3 minutes.

Add your flour to this and stir.  I used navy bean flour this time, but you can use unbleached white flour, brown rice flour -- whatever you want.  Arrowroot might even work, although it would change the final texture somewhat.

Cook and stir for a minute or two, then add the chicken stock.  You can choose water, vegetable stock, or even extra milk if you want.

Use this liquid to deglaze the pan, scraping all those brown bits of goodness up.  Then add the milk.

Stir it until it's a smooth sauce.  Add a little extra stock or milk if it's too thick.

Then add the cheese, finely grated.  Stir again until the cheese is melted and the sauce is smooth.  Then, it's time to serve!

Drain the pasta, slice the chicken, and mix it together.