Preheat the oven to 425ºF.
Wash the potatoes and dry them with a paper towel, and cut the potatoes in half.
Place in a bowl and add the olive oil, salt, cayenne pepper, and paprika; toss until the potatoes are evenly coated with spices.
Transfer the potatoes to a baking pan and spread them out into one layer.
Meanwhile, cut off about a quarter-inch from the top of the garlic head to expose some of the cloves inside.
Place the garlic on a piece of foil. Drizzle with olive oil, wrap in the foil, and place it on the baking tray with the potatoes.
Roast for 45 minutes to 1 hour or until browned and crisp.
Remove the baking pan from the oven. Unravel the foil and squeeze out the baked garlic in a small pan.
Mash the baked garlic with a fork until smooth, add 2 tbsps. of olive oil and 5 sprigs of fresh thyme or a stalk of rosemary.
Heat the small pan for about a minute or two and pour the garlic mixture over the potatoes. Mix until all the potatoes are well coated with the garlic mixture.