Wash and scrub the potatoes thoroughly. Pat them dry with a towel.
Using a sharp knife, carefully slice the potatoes crosswise at 1/4-inch intervals, stopping about 1/4 inch from the bottom to keep them intact. You can place the potatoes between two chopsticks to prevent cutting all the way through.
In a small bowl, mix together the melted butter, minced garlic, thyme, paprika, salt, and pepper.
Drizzle the garlic butter mixture over the potatoes, ensuring it seeps into the cuts. You may need to use a brush to get it into the crevices.
Sprinkle the grated Parmesan cheese generously over the potatoes, allowing some to fall into the sliced openings.
Place the potatoes on a lined baking sheet and roast them in the preheated oven for about 45-50 minutes, or until the edges are crispy and the insides are tender.
Remove the potatoes from the oven and let them cool for a couple of minutes.
Garnish with fresh chopped parsley before serving.
Notes
Use chopsticks to prevent cutting through the potatoes completely.