Prepare the potatoes. Place the potatoes in a baking dish that will hold them snugly, in a single layer, and with enough height to cover them with the oil, without getting too near the top edge. Set aside.
Prepare garlic and add it to the potatoes. Peel the garlic cloves, and then use a paring knife to cut off the root ends. Slice them vertically down the center and use the tip of the knife to remove the inside root. Add the garlic cloves to the potatoes, making sure they are evenly dispersed.
Add oil and bake. Pour the oil over the potatoes and garlic. It should cover them, but barely. Place the baking dish with the potatoes on a baking sheet, and then in the preheated 225°F oven, uncovered, for 2 hours. Then turn the heat to 400°F, and cook for another 10 minutes -- at this point the oil should be sizzling a bit.
Cool. Remove them from the oven and let them cool at room temperature in the oil.
Remove potatoes and garlic from oil and mash. Use a slotted spoon to transfer the potatoes and every bit of the garlic to a mixing bowl. Use a large fork to mash everything together. (I prefer the potatoes to be chunky for this dish.)
Season. Season generously to taste with salt and pepper. (Here's How.)
Save the garlic infused oil -- you can use it for all sorts of cooking for the next couple of days.