Preheat the oven to 400°F (200°C). Lightly grease a baking dish or line it with parchment paper.
Pat the cod fillets dry with paper towels. Season both sides with 1/4 tsp salt and 1/8 tsp black pepper.
In a small bowl, combine the panko breadcrumbs, minced garlic, 1 tbsp parsley, 1 tbsp basil, 1 tsp thyme, and 2 tbsp olive oil.
Place the seasoned cod in the center of the baking dish. Press the breadcrumb mixture evenly onto the top of each fillet.
Arrange the halved cherry tomatoes around the cod. Season the tomatoes with the remaining 1/4 tsp salt and 1/8 tsp pepper.
Bake for 12 to 15 minutes, or until the fish flakes easily with a fork and reaches an internal temperature of 145°F.
While the fish bakes, whisk together the herb oil: 2 tbsp olive oil, 1 tbsp mixed fresh herbs, 1 tbsp lemon juice, and a pinch of salt.
Remove the cod from the oven. Drizzle the fresh herb oil over the fish and blistered tomatoes before serving.