Melt butter and olive oil in a one-quart saucepan set over medium heat.
Add potatoes, onions and thyme and give a good stir.
Cover pan and reduce heat to medium-low.
Let the vegetables “sweat” for about 10 minutes, stirring often.
Remove lid and add chicken broth.
Cover pan tightly and let soup simmer 15 minutes.
Season with salt and pepper, then add the Parmigiano Reggiano.
Remove from heat and purée soup till smooth, using a blender or food processor.
Garnish and serve piping hot.
Garnish: Freshly chopped parsley and shavings of Parmigiano Reggiano made by pulling a vegetable peeler over a wedge of the cheese