Prepare the Vegetables:
Peel and dice the potatoes. Set aside. Dice the onion, mince the garlic, and finely chop the jalapeños, removing the seeds if you want to reduce the heat.

Sauté the Vegetables:
In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion and cook for 3-4 minutes, until soft and translucent. Add the minced garlic and jalapeños, cooking for another 1-2 minutes until fragrant.

Add the Potatoes and Seasonings:
Stir in the diced potatoes, smoked paprika, and cumin. Cook for another 2 minutes, letting the spices toast slightly and infuse the potatoes.

Simmer the Soup:
Pour in the chicken or vegetable broth, making sure the potatoes are mostly covered. Bring the mixture to a boil, then reduce the heat to low and let it simmer for 15-20 minutes, or until the potatoes are fork-tender.

Blend the Soup:
Once the potatoes are cooked, use an immersion blender to blend the soup until it reaches your desired consistency. You can blend it completely for a smooth soup or leave it a little chunky for more texture. If you don’t have an immersion blender, carefully transfer the soup in batches to a blender and blend until smooth.

Add Milk and Cheese:
Stir in the milk and shredded cheddar cheese, allowing the cheese to melt into the soup. Continue to cook over low heat for 5-7 minutes, stirring occasionally, until the soup is creamy and well-combined. Taste and adjust the seasoning with salt and pepper.

Serve:
Ladle the soup into bowls and top with extra shredded cheddar cheese, fresh cilantro or green onions, a dollop of sour cream, and crumbled beef (if desired). Serve with crusty bread for dipping.