Heat the olive oil in a skillet over medium heat. Add the onion and carrot, then cook for 4 minutes until the onion softens.
Stir in the garlic, sweet paprika, and smoked paprika. Cook for 1 minute more to toast the spices without burning them.
Transfer the onion mixture to the slow cooker. Add the potatoes, mushrooms, vegetable broth, and tomato paste. Stir to combine.
Cover and cook on low for 7 hours or high for 4 hours, until the potatoes are fork-tender.
Taste and season with salt and black pepper. Serve hot, topped with chopped fresh parsley.