Preheat oven to 425 F. Grease an oven safe baking dish with cooking spray. Thinly slice potatoes, leaving the bottom intact. Place potatoes in baking dish and drizzle with olive oil, salt, and pepper. Bake for 30 minutes.
While the potatoes bake, melt vegan butter over low heat. Add garlic and cook until fragrant. Add thyme, oregano, and rosemary and stir until well incorporated into the mixture. Stir in the nutritional yeast and vegetable broth, whisking it until it's smooth. Set the mixture aside because it will thicken slightly as it cools.
Remove potatoes from oven and drizzle with sauce. Return to oven for 30-40 more minutes or until crispy. Top with remaining sauce and fresh parsley to serve.