A food processor makes easy work of fish cakes, although they can also be made by hand.
Preheat oven to 200 degrees. Heat 1 tablespoon olive oil in a skillet over medium heat. Add onion, 1/2 teaspoon salt, and 1/8 teaspoon pepper. Cook until onions are translucent, about 5 minutes. Set aside.
Cut fish into large chunks; pulse in a food processor to coarsely chop. Transfer to a medium bowl. Add onion, tarragon, egg, and Tabasco, and combine well. Add remaining salt and pepper. Form 8 patties (3 inches each); dredge them in breadcrumbs, shaking off excess.
Heat 1 tablespoon oil in a large skillet over medium-low heat. Cook 4 patties until browned, about 4 to 5 minutes on each side. Remove to a baking sheet, cover with aluminum foil, and keep warm in oven. Wipe out skillet, return to heat, and add remaining olive oil. Cook remaining patties, and serve immediately with tartar sauce.