In a heavy-bottomed pot with olive oil and butter, sauté peeled potatoes cut into cubes for about 3-4 minutes. Add peeled and halved garlic, stir and fry together for about 2 minutes.
Pour in hot broth, add turmeric and bring to a boil. Reduce heat, cover and cook for about 10-15 minutes until potatoes are tender.
Break off the tough and pale ends of the asparagus (they will break naturally at the right spot), discard the ends. Rinse the stems, cut into thin slices, keep the tips whole. When potatoes are tender, add the asparagus (tips and stems) and cook over low heat for about 1 minute.
Add dill and remove from heat. Place sour cream in a bowl and gradually add a few tablespoons of soup broth at a time, stirring. Add this tempered sour cream to the pot of soup and stir. Serve with crumbled feta and chives.