In a large bowl toss the potatoes, onion and garlic in 4 TBS (60ml) of oil with half of the salt and pepper.
Heat the remaining 2 TBS of oil in a 10" (26cm) skillet over medium heat until the surface of the oil starts to shimmer. Add the potato and onion mixture along with all of the oil in the bowl and spread into an even layer. Keep the bowl handy for the eggs.
Reduce the heat to medium low, cover the pan and cook until the potatoes are cooked through and tender, about 15-20 minutes depending on how high the fire is and how thick the potatoes are. Gently stir the mixture every 5 minutes or so to promote even cooking and to prevent the bottom layer from browning too much. a little color is OK. Test for doneness by poking a potato with the point of a small knife.
While the potatoes are cooking, whisk the eggs with the remaining salt and pepper in the bowl you tossed the potatoes in.
Once the potatoes are cooked remove the pan from the heat and let it cool for 5-10 minutes. Once the potatoes have cooled slightly, tip them into the bowl with the eggs and stir to combine.
With the skillet back on medium heat, add the egg and potato mixture. Stir gently so as not to break up the potatoes until the eggs are halfway set, then reduce the heat to medium low, cover the pan and cook until the eggs start to puff up around the edges. This will take about 10 minutes depending on how high you have the fire. A lower fire will take longer to cook and result in a lightly browned tortilla. A higher fire will cook faster and produce a deeper brown tortilla. Either is fine and is a matter of personal preference.
If there is still some liquid eggs on top after the edges begin to soufflé, use a rubber spatula to lift up the edge of the tortilla and tilt the pan to let the uncooked eggs have their turn to cook.
Using your spatula, loosen the tortilla so it slides easily when you shake the pan. Slide it on to a large plate, cover it with another large plate and quickly, with the courage of you convictions, flip the tortilla over. Slide it back into the pan and using your spatula tuck it in around the edges to make it look pretty. Continue to cook, uncovered another 5 minutes or so to set the bottom crust.
Slide the tortilla on to a cutting board and allow it to cool at least 15 minutes before slicing it into wedges and serving with a dollop of allioli.
For the allioli, mix together all the ingredients to thoroughly combine. Refrigerate until ready to use.