Preheat your oven to 425°F (220°C). In a mixing bowl, toss the halved baby potatoes with 1 tablespoon of olive oil, a pinch of salt, pepper, and half of the minced garlic. Spread the potatoes cut side down on a baking sheet or oven-safe skillet. Roast for about 25-30 minutes until golden brown and crispy on the outside, tender inside.
While the potatoes roast, melt 2 tablespoons of butter with 1 tablespoon of olive oil in a small saucepan over medium heat. Add the remaining garlic and sauté until fragrant and lightly golden, about 1-2 minutes. Stir in the lemon zest, lemon juice, and fresh thyme leaves. Season with salt and pepper to taste. Remove from heat and set aside.
Pat the cod fillets dry with paper towels and season both sides generously with salt and pepper. Once the potatoes are roasted, create space on the baking sheet or transfer them to a plate temporarily. Place the cod fillets skin-side down on the skillet or baking sheet. Spoon the lemon garlic butter sauce over each fillet generously.
Return the skillet or baking sheet with cod and potatoes to the oven. Bake for 10-12 minutes or until the cod is opaque and flakes easily with a fork.
Remove from the oven and sprinkle with fresh chopped parsley for a burst of color and freshness. Serve the cod with the crispy potatoes alongside, spooning any extra lemon garlic butter sauce over the top for maximum flavor.