Heat olive oil in a large pot over medium heat. Sauté diced onion for 5 minutes until translucent. Stir in minced garlic and cook for 1 minute.
Add chicken broth and diced potatoes. Bring to a boil, then reduce heat and simmer for 15 minutes.
Add softened cream cheese, shredded cheddar cheese, pepper jack cheese, and milk. Stir until melted and creamy.
Blend the soup with an immersion blender for a smoother texture, if desired.
Add drained diced jalapeños, smoked paprika, salt, and pepper. Simmer for another 5 minutes.