Preheat the oven to 400 degrees Fahrenheit. Place the whole jalapeños on a baking sheet and cook for 22-25 minutes, flipping over after 10 minutes, until the peppers are charred with brown/black spots on the outside, have collapsed and are tender. Remove the peppers from the oven and place them in a bowl covered with a plate (this steams them and makes the skins easier to remove).
Meanwhile, prep the other jalapeño hummus ingredients. To a food processor, add the tahini, garlic, and lemon or lime juice. Process until smooth, scraping down the sides as needed.
Add the chickpeas or white beans, cumin, cilantro or parsley, and salt. Blend until smooth, scraping down the sides as needed.
Remove the stems and skins from the jalapeños. Cut them open and scrape out the seeds. Add the peppers to the food processor and process until smooth.
Slowly add the oil while the food processor is running. Season to taste with salt, pepper, additional lemon or lime juice, and additional olive oil or warm water as needed to reach your desired texture (hummus will thicken a little bit after it cools).