Heat the olive oil in a large pot over medium heat. Add the onion and garlic and cook until the onion softens.
Add the sliced mushrooms and cook until they release their liquid and start to brown.
Stir in the cubed potatoes, sliced carrots, and Hungarian paprika until the vegetables are coated.
Pour in the vegetable broth and bring the mixture to a boil.
Reduce the heat, cover the pot, and simmer until the potatoes are tender.
Season with salt and black pepper. Ladle into bowls and top each serving with a spoonful of sour cream and a sprinkle of parsley.