Heat oil in a wide, deep skillet or Dutch oven over medium-high heat. Add onion to the pan. Cook about 5 minutes, stirring occasionally.
Add garlic, stir and continue to cook as you chop potatoes in 1-inch chunks and add them to the pan.
Trim cauliflower into pieces about as big as the potatoes. When the potatoes have cooked 10 minutes, add the cauliflower, lots of salt and pepper and green chiles. Trim the stem from the jalapeño, mince the pepper and add as much of it as you like.
Add chicken broth or enough water to make 6 cups of liquid. Bring to a boil, lower heat to simmer, cover and cook 15 minutes. Potatoes and cauliflower should be tender.
Remove from heat. Working in several batches, add soup to a large mixing bowl and blend until smooth. Return all blended soup to pan and heat to boiling.
When the soup is hot throughout, remove from heat and stir in the cheese. Alternatively, you can serve the soup with the cheese sprinkled on top.Servings: 4 to 6