roasted garlic aioli: Place all the ingredients into a mixing bowl and whisk together. Cover and set aside.
falafel patties: Place the dry beans in a mixing bowl and fill with enough water to completely submerge the beans. Allow beans to soak overnight (at least 12 hours). Drain and set aside.
Place garlic, onion, parsley, and cilantro into a food processor and pulse 4 to 5 times. Add chick peas followed by the remaining ingredients and process until finely ground and the mixture can hold together. Transfer to a mixing bowl, cover and refrigerate for 30 minutes.
Once the mixture has chilled, divide it into 4 equal portions and create 4 patties. Place onto a parchment lined baking sheet and refrigerate for another 30 minutes.
Fill a saucepan with 2 inches of oil, once the oil is hot, carefully add 1 to 2 patties at a time and fry for about 3 to 4 minutes on each side. Drain onto a paper towel, lightly season with salt and pepper and repeat until all patties have been fried.
quick pickled red onion: Pour sugar and salt into the vinegar and whisk together until sugar and salt dissolves. Add remaining ingredients, stir, cover and set aside. Allow red onions to ‘pickle’ for at least 30 minutes to 1 hour.
To assemble: Cut each bun crosswise and toast. Spread the aioli onto each bun and top with a falafel patty. Top patty with sliced cucumbers and pickled red onions, and the aioli smeared bun tops and serve immediately.