Preheat oven to 180C/350F. Slice off the tops off the garlic heads and then discard the papery layers on the outside of the garlic. Place the three heads of garlic on a large sheet of foil and drizzle oil over. Gather up the corners and make into a little sealed foiled package and roast for 1.5 hours - the garlic should be very soft and dark. You can do this 1 week ahead of time.
Peel the potatoes and cut into large chunks (slightly bigger than bite sized). Place a large pot of water onto boil and add the salt and bicarb. Add the potatoes and cook for 10 minutes or until starting to get tender. Drain into a colander and rinse the potatoes well.
Preheat oven to 220C/428F and line two large baking trays with parchment. Put the pot back on the stove add the duck fat to the pot and squeeze out the caramelised garlic from the skin and mash the garlic into the oil and heat. Add in the potatoes and toss them gently to coat with the garlicky duck fat. Then add the parmesan cheese and toss to coat. Spread out onto the baking trays in a single layer and roast for 40 minutes.