Dice the potato into 1-inch pieces.
Add the diced potato & drained/rinsed canned chickpeas into a medium saucepan & cover with water. Add a couple dashes of salt to the water.
Bring the water to a boil, then cover the pan with a lid & reduce the heat. Simmer over low-medium heat, covered, for about 15 minutes (until the potatoes are softened).
While potatoes & chickpeas are simmering, you can prep the other ingredients for your fondue night. Slice the bread into small pieces, wash & cut any fresh veggies that will be used, etc.
After 15 minutes, drain water from the potatoes & chickpeas in a colander, and then add them into a blender.
At this point, I added the dry white wine and lemon juice to the empty saucepan, and simmered the wine & lemon juice on low heat for about 5-10 minutes to try to burn off some of the alcohol. (this step can be skipped if you don't mind the alcohol staying in the fondue or if you are using vegetable broth). After it was simmered, I added it into the blender.
Return your saucepan to the stove, heat a teaspoon of oil, and add the minced garlic to the pan. Fry for about 1 minute, and then add into the blender.
Add all remaining ingredients to the blender & blend on high until the sauce is smooth.
Return the sauce to the saucepan and cook the sauce over medium heat for about 5-10 minutes, or until it's slightly stretchy & elastic.
Taste the sauce, and add more seasonings as needed (salt, lemon juice, crushed red pepper and/or regular pepper, soy sauce, dijon or wholegrain mustard, etc)
Transfer the sauce to your fondue pot and serve with bread cubes, fresh veggies, fruits, roasted potato slices, or vegan sausages, etc. (if you don't have a fondue pot, you can just transfer it to serving dish- it's more fun with a fondue pot and a fondue pot will keep it warm- but not technically "required").