Peel the potatoes and chop them into large chunks. Boil them until they can be easily pierced.
Meanwhile, prepare the garlic (10 cloves is a lot of peeling!) If you don't have a garlic press, mince the garlic.
Drain the potatoes and mash them slightly in the pot. Transfer the potatoes to a food processor. Add the minced or pressed garlic and the salt. Whizz the potato mixture just to combine. Then add half the vinegar and half the olive oil. Process for a few seconds, then add the remaining oil and vinegar, along with the ground pepper. Puree one more time for good measure.
You should have a fairly smooth mixture with a texture reminiscent of mashed potatoes. If necessary, add more olive oil and vinegar to moisten, but be cautious.
Serve this dip warm or at room temperature with fresh pita bread.