Place the chickpeas in a large bowl. Cover them with plenty of water (2 inches above the level of the chickpeas to allow them to expand) and leave to soak overnight (or for a minimum of 12 hours). Drain and rinse well before use.
Peel and quarter the onion and add to the Thermomix bowl with the peeled garlic cloves. Chop for 5 seconds / speed 5.
Add all the other ingredients (see note) to the Thermomix.
Mix for 30 seconds / speed 5. Scrape, stir and repeat 3-4 times until you have the correct consistency. You want it to be a rough paste, still with some texture.
Transfer to a bowl, cover and refrigerate for a minimum of 1 hour.
When ready to make the falafels, use a cookie scoop or spoon to portion 2 tablespoons of mixture. Use wet hands to form balls. Roll in sesame seeds, if desired.
Set aside until ready to cook.
Heat the oil in a large skillet until hot. You want the oil to be deep enough to cover half the falafel, so you only need to turn it once, so the amount you use will depend on the size of your skillet and your falafel.
Fry for around 2-3 minutes each side until a deep brown color.