In a medium pot, melt the butter in the EVOO, 2 turns of the pan, over medium-low heat. Add the onion and garlic and cook until softened, 10 minutes. Add the boiled potatoes and milk and mash together. Season with pepper and the thyme, then stir in the chicken broth. Stir in the reserved vegetables and heat through, about 2 minutes. Stir in the cheese. Thin the soup with a little water if desired. Pass the crusty bread and extra cheese around the table.