Coat the bottom of a large pot with the oil and place it over medium heat. Give the oil a minute to heat up, then add the onion. Sweat the onion for about five minutes, stirring often, until it begins to soften.
Stir in the garlic, jalapeño, cumin, and oregano. Cook the mixture for about a minute, stirring constantly, until it becomes very fragrant.
Stir in the broth and tomatillos. Raise the heat to high and bring the liquid to a boil.
Lower the heat and allow the soup to simmer for about 20 minutes, until the tomatillos are very soft. Remove the pot from heat and stir in the cilantro.
Blend the soup, either using a hand blender, or by transferring it in batches to a blender then returning it to the pot. Always use caution when blending hot liquids.
Season the soup with salt and pepper to taste.
Ladle into bowls and serve with toppings of choice.