Preheat the oven to 425 degrees F. While oven is heating, dry turkey with a paper towel. Drizzle with 1 tablespoon olive oil and rub to cover all parts of skin and meat. Season very generously on all sides with salt and pepper.
Place turkey breast on the rack of a roasting pan or on a baking sheet and roast for 15 minutes. Without opening oven, lower heat to 350 degrees F and continue roasting for about one hour, or until a cooking thermometer reads 155 degrees F when inserted into the thickest portion of the breast.
When cooked through, remove from oven, cover with foil, and let stand for 20 minutes. Using a sharp knife, slice in between the breastbone and turkey breast meat. Working away from you, slice across and down the length of the breast, using your other hand to pull the meat away from the bone as you cut.
Meanwhile, bring a large pot of water to boil over high heat. Cut potatoes in half lengthwise and add to the pot. Reduce heat to a simmer and cook, uncovered for 30 minutes or until a sharp knife pierces skin and potato easily. Remove from heat, drain and cool briefly in a colander. When potatoes are cool enough to handle but still slightly warm, transfer to a large bowl and season with salt and pepper.
In a food processor, combine garlic and parsley. Pulse to combine until parsley leaves are well broken down. Slowly drizzle in ½ cup of olive oil until all is incorporated. Scrape down sides and season to taste with salt and pepper.
Toss potatoes in the parsley pistou and serve alongside sliced turkey.