Preheat oven to 425 degrees and line a baking sheet with parchment paper.
Use a mandolin to slice potatoes into quarter inch thick rounds. In a medium bowl, combine potatoes with melted butter, garlic, minced thyme, a pinch of salt and a few grinds of pepper.
Shingle the potatoes into two rectangles on the baking sheet, about 4x6 inches.
Roast potatoes until just tender, about 30-35 minutes. Rotate pan after 15 minutes.
Meanwhile, pat cod dry with a paper towel. Season with salt and pepper.
Remove potatoes from oven. Place one piece of cod on top of each rectangle of potatoes. Top with pieces of butter, 2 sprigs of thyme each, and lemon slices.
Return to oven for about 15 minutes until the fish flakes easily with a fork and reaches 140 degrees.
To serve, use a spatula to carefully transfer to plates.