Heat the oil in a large sauce pan over medium-high heat, add the chicken (seasoned with salt and pepper) and brown, abut 3-5 minutes per side, before setting aside.
Add the onion and garlic and saute until the onions are tender and the everything is lightly browned, about 3-5 minutes.
Sprinkle in the thyme and flour and cook for a minute.
Add the broth and the wine, deglaze the pan by scraping the brown bits off of the bottom of the pan with a spoon while the broth and wine are sizzling when added.
Mix the asiago into the sauce and season with salt and pepper to taste.
Add the chicken, cover (with a lid or foil) and roast in a preheated 400F oven for 15 minutes OR turn the heat down to medium-low and simmer on the stove top for 15 minutes.
Notes
Option: Start by cooking 4 strips of bacon, set aside and cook the onion in the bacon grease and add the crumbled bacon to the sauce after roasting!