For the extra tangy tartar sauce, whisk together the mayonnaise, cornichons, capers, Dijon mustard, lemon juice and parsley until well combined and set aside.
On a large plate, season the cod with salt all over and then sprinkle with enough flour and toss so all filets are coated completely.
In a large bowl, whisk the ¾ cup flour, cornstarch, Old Bay, lemon zest, baking powder and 1 teaspoon salt (Diamond Crystal kosher, but adjust based on your salt’s saltiness) until combined well.
Heat a Dutch oven or large cast-iron skillet over low heat. In batches, toast one side of each of the brioche slices (or inside of brioche buns) just enough to get a golden to golden brown sheen, about 1 minute (they toast quickly, so don’t walk away). Place them, toasted side up, on your cutting board or counter.
Pour about 1-inch worth of oil into your Dutch oven or skillet and heat over medium-high until it registers 350º F with an instant-read or fry thermometer. Toggle the heat to keep the temperature at 350.
Pour the egg into the flour mixture and whisk well to combine and dissolve any pesky clumps. Slowly pour and whisk the beer into the batter.
Fry the fish two pieces at a time. To do so, dip two filets in the batter, lift them out, let the excess batter fall off then place in the fry oil. Fry, turning once or twice to crisp and brown evenly, until batter is golden brown and the middle of fish is cooked through and registering 145º F with an instant read thermometer. Transfer to a cooling rack, season with salt and repeat with remaining filets.
Slather the tartar sauce on the inside of the bread slices, place the fried cod on the bottom pieces, top the fish with lettuce leaves and the top brioche slice then serve.