Rinse and dry the fingerling potatoes thoroughly. Trim off any blemished parts but leave the skins on. Cut each potato lengthwise into halves.
In a large mixing bowl, combine the potatoes. Drizzle with olive oil and add in the minced garlic, 1/2 teaspoon of kosher salt, thyme, and black pepper. Using your fingers or a large spoon, mix everything well for even coating.
Spread the potatoes onto a large rimmed baking sheet or roasting pan, ensuring the cut sides face down for a nice sear. Avoid overcrowding the pan.
Roast in the preheated oven for about 30 to 40 minutes, depending on the size of the potatoes. For best results, turn them twice, spreading them back out into an even layer each time. They should be golden brown and easily pierced with a fork.
Once cooked, remove them from the oven. Sprinkle with the remaining 1/4 teaspoon of kosher salt and the fresh parsley. If desired, add the grated Parmesan cheese and give it a gentle stir. Serve while hot and enjoy with a main dish of your choice!