In a large, heavy-bottomed pot, heat the olive oil over medium heat. Add the diced jalapeños, chopped onion, and minced garlic. Sauté these ingredients until they are tender and the onion becomes translucent, which should take about 5-7 minutes. Stir occasionally to prevent sticking.
Gradually pour in the chicken or vegetable broth, stirring to combine, and then bring the mixture to a gentle simmer.
Reduce the heat to low and incorporate the softened cream cheese into the simmering broth. Stir continuously until the cream cheese is completely melted and well blended into the liquid.
Add the shredded sharp cheddar cheese to the pot in small amounts, stirring continuously until fully melted. Then pour in the milk, followed by the smoked paprika and ground cumin. Mix everything together until it is well combined and creamy.
Season the soup with salt and freshly cracked black pepper to your taste. Allow the soup to simmer for an additional 5 minutes, which will help the flavors meld beautifully.
If desired, use an immersion blender to puree the soup to your preferred consistency—smooth for a creamy base or leave it chunky for added texture and heartiness.
Ladle the hot soup into bowls and garnish each serving with a sprinkle of fresh chopped cilantro and a handful of crispy tortilla strips on top for a delicious crunch.
Notes
Adjust the heat by removing the seeds from the jalapeños.