Thinly slice the onion. It works best to use a mandolin to get them even, but if you're great with a knife then try it out! They should be thin enough that you can sort of see through them.
Pour the nondairy milk into a shallow dish and whisk with apple cider vinegar. Soak the onions in this mixture for 15 minutes. In a separate mixing bowl combine the flour with smoked paprika, cayenne, salt, and pepper.
Heat your frying oil in a heavy-bottomed pot or deep fryer to 365°F to 375°F.
Only when the oil has reached it's correct temperature, you can use a pair of tongs and take a handful of onions from the liquid and coat evenly with the flour mixture. Place a batch into the oil. You might need to use a fork to move them around in the oil a bit just to keep them from sticking to each other. They only take 2 minutes to fry up, then remove that batch with the tongs and lay out onto paper towel. Continue doing batches until all the onions are used up.