1. Make the Tartar Sauce: Stir together all of the tartar sauce ingredients in a small bowl. Cover and refrigerate for at least 1 hour before serving.
2. Prepare the Fish Sticks: Place the flour, eggs, and bread crumbs in three separate shallow bowls. Working in batches, dredge the cod in flour, shaking off the excess. Then, dip in the egg, letting any excess run off. Finally, coat with the panko breadcrumbs and place on a parchment-lined baking sheet. Repeat until all of the pieces of cod have been breaded.
[DO AHEAD: At this point, the baking sheet can be wrapped tightly with plastic wrap and refrigerated for up to 1 day. Alternatively, you can place the baking sheet in the freezer, and once the fish sticks are completely frozen, transfer to a freezer-safe resealable plastic bag and freeze for up to 3 months. The fish sticks can be cooked directly from the freezer, however the cooking time will increase slightly.]
3. Pour enough vegetable oil into a large skillet to cover the bottom (I used a 12-inch cast iron skillet) and place over medium-high heat. Once the oil is shimmering, fry the fish sticks in batches (don't overcrowd the pan), turning them so that they evenly brown, about 6 to 8 minutes total. Transfer the fish sticks to a paper towel-lined plate and sprinkle with salt. Serve immediately.
Baking Alternative: If you prefer baked fish sticks, you can bake the prepared sheet of fish sticks in a 450-degree oven until the fish is cooked through, about 10 to 12 minutes, turning once during baking. To facilitate browning, spray the fish sticks with non-stick cooking spray or drizzle with olive oil before baking.