Heat olive oil in a skillet over medium heat. Add diced yellow onion and minced garlic, cooking for about 5 minutes until translucent.

Transfer the sautéed onion and garlic to your slow cooker. Add diced potatoes, sliced carrots, diced celery, and smoked sausage. Stir to combine.

Pour in vegetable broth. Season with dried thyme, paprika, and salt and pepper. Stir everything thoroughly.

Cover and cook on low for 6-7 hours or high for 3-4 hours, until vegetables are tender.

Mash a portion of the potatoes in the soup for a creamier texture while keeping some chunks.

Stir in milk or heavy cream and let the soup warm for an additional 10 minutes.