Season the chicken with salt, pepper, mustard powder, garlic powder, oregano, and dried parsley.
Heat the oil in a large non-stick skillet over medium-high heat and brown the chicken breasts on both sides, about 3-5 mins on each side until fully cooked. Transfer to a plate and keep warm.
Melt the butter in the same skillet, over medium-high heat and add the minced shallots and garlic. Saute until translucent, about 3 mins. Add the white wine and deglaze the pan, scraping to pick up all the brown bits and pieces stuck to the bottom. Simmer until reduced by half, about 3 mins.
Pour in the chicken broth and add the Boursin cheese to the skillet. Cook until the cheese is melted and the sauce thick, about 2 minutes.
Whisk in the parmesan cheese, half and half, fresh thyme, and dried parsley. Simmer on low for 5 more minutes. Check the seasoning and add more salt, if needed.
Return the chicken to the skillet and cook until heated through.