Preheat your oven to 350. Slice off the very top of the garlic, keeping the rest of the garlic intact. Place the head of garlic, exposed side down, into a small glass pyrex dish. Drizzle with olive oil and cover the top tightly with tin foil. Place into the oven to bake for 45 minutes.
While your garlic is roasting, combine all of the fries ingredients into a bowl and whisk until smooth.
Place two tablespoons of oil into a large skillet over medium high heat. Once the oil is very hot, slowly pour the batter into it. Once it starts to slightly bubble after a minute or two, take a whisk and stir it continuously and vigorously until thickened, about 7 minutes.
Remove it from the heat and transfer the thickened batter into a glass container greased with a little oil. Place into the refrigerator to cool and set.
After 45 minutes, pull your garlic out of the oven. Flip it over, and spoon some of the oil that’s collected in the bottom of the glass dish over the top. Replace the foil and bake for an additional 30-45 minutes, until golden brown and bubbly.
Allow the garlic to cool completely, then separate and squeeze the roasted garlic into a bowl. Add in the rest of the aioli ingredients, then drizzle the leftover olive oil into it. Whisk until well combined.
By now, your chickpea batter should be firm enough to slice. Slice it into whatever shape you want and set aside.
If deep frying, place plenty of vegetable oil into a small saucepan. Heat it over medium-high heat for about 7 minutes. Insert a wooden spoon into the pot, touching the bottom of the pot with it. If bubbles form around the spoon immediately, you are ready to fry.
Place a few of the fries into the hot oil (no more than six), ensuring that they do not stick together. Fry for a few minutes until golden brown. Transfer to a paper towel to drain, then sprinkle with salt. Repeat with the rest of the batter.
If pan-frying, place a couple of tablespoons of oil into a saute pan over medium-high heat. Fry the pieces for a few minutes on each side until golden brown. Sprinkle with salt while piping hot.
Serve immediately with the roasted garlic aioli and chopped fresh parsley.