Finely chop the onions and garlic. Peel the potatoes and cut finely.
Heat butter and oil in a large pot. Sauté onions, garlic and potatoes until translucent. Deglaze with wine, add stock and bring to a boil, stirring, for 10-15min. Season with salt and pepper and add the Glarner Grüessli. While the soup is simmering, sort out the arugula leaves, wash and dry, setting aside a few leaves for garnish. Rucola leaves coarsely chop, shave the white Stöckli with truffle.
Add the arugula and the cream to the soup and puree everything very finely, finally season with salt and pepper and serve the soup hot garnished with truffle sticks and arugula.