DO NOT wipe the skillet.
Add butter to skillet and melt over medium-high heat.
Add onions and cook for 3 minutes, or until softened.
Stir in garlic, salt, and pepper; cook for 30 seconds, or until fragrant.
Add wine and bring to a simmer, scraping the bottom of the skillet to mix the brown bits into the liquid; cook for 4 to 5 more minutes, or until half of the wine has reduced.
Stir in thyme and half-and-half.
Reduce heat to slowly bring to a boil; place chicken breasts back in the skillet and leave to simmer and thicken for about 4 minutes.
Remove skillet from heat.
Garnish with fresh chopped parsley.