In a large pot, melt the butter over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Add the minced garlic and cook for an additional minute, stirring frequently to avoid burning.
Toss in the diced potatoes, along with the vegetable broth, dried thyme, smoked paprika, salt, and pepper. Bring to a boil, then reduce heat to simmer and cover. Cook for about 15-20 minutes or until the potatoes are fork-tender.
Once the potatoes are tender, use an immersion blender to carefully puree the soup until smooth. (Alternatively, you can transfer the soup in batches to a blender; just ensure to vent the lid slightly to avoid pressure build-up.)
Stir in the heavy cream and cheddar cheese until melted and combined. Taste and adjust seasoning as desired.
Serve hot, dolloping sour cream on top of each bowl and garnishing with chopped green onions and crispy kale crumbles.
Notes
For a thicker soup, blend longer or add more potatoes.