Add the chicken breasts and brown them on each side until just barely done, 8 to 10 minutes per side. Remove the chicken from the pan and set aside.
Pour the dry vermouth into the same skillet and stir, deglazing the pan by scraping up any browned bits. Simmer for 3 minutes.
Add the garlic powder and whisk in the softened cream cheese. The sauce should be the consistency of heavy cream. Add a little chicken stock or milk if it’s too thick.
Return the chicken with any accumulated juices to the pan. Check for seasoning.
To serve, spoon some sauce over the chicken and garnish with green onions. Serve with extra sauce on the side.