Preheat the oven to 400º F.
Remove the cod fillets from the fridge, pat them gently with a paper towel, and let them sit on the counter at room temperature for about 15-20 minutes. Bringing the fish to room temp helps you get a more even cook.
Pop the butter, oil, tomato paste, fresh herbs, capers, garlic, salt, and pepper into a small mixing bowl. Mash and mix it all together until you have yourself a nice little compound butter!
Place some lemon slices down into the baking dish.Now set your fillets over the lemon slices so they are sitting on top of them. You only need about one or two slices of lemon per filet.
Divide the compound butter up evenly and spoon the mixture over each filet. Press down on the butter and smother the filets with it so the tops are fully covered.
Place a slice of lemon or two on top of each fillet, and then pop the grape tomatoes into the pan.
Transfer the pan to the oven and bake for 12-15 minutes; be sure to check on the fish after 12 minutes. You don’t want to overcook it!
When it’s ready, remove it from the oven, spoon over some of that pan sauce, and garnish with some fresh basil and parsley.