Place flour in a shallow baking dish or plate; stir in salt and pepper. Dredge each filet in the flour mixture, shaking off excess.

In a large skillet, heat 2 tablespoons of the neutral oil over medium-high heat until hot (but not smoking – see Tip below), about 2 minutes. Place 3 fillets in skillet. Sauté, without moving, until golden brown, around 3 to 3 1/2 minutes per side. Remove from pan and set aside. Repeat process with remaining 2 tablespoons of neutral oil and 3 fillets.

Return the pan to medium-high heat and add 1 tablespoon olive oil and 1 tablespoon of butter. Once the butter melts, add chopped shallots and sauté for around 30 seconds.

Stir in white wine, scraping up any browned bits on the bottom of the pan. Bring to a medium boil and cook until the liquid is reduced by half, around 3 minutes.

Stir in the broth, lemon juice and capers. Bring to a slow boil and cook for another minute. Reduce heat to medium and whisk in the remaining 2 tablespoons of butter. Cook, stirring occasionally, until the pan sauce thickens slightly, about 3 to 5 minutes.

Stir in the chopped green onion and artichoke hearts. Return the fish fillets to the pan (with the sauce) and cook just until the fish is warmed through, about 2 minutes.

Serve immediately, placing fillets on individual dinner plates (or one large serving platter) and spooning sauce over the top.

Garnish with lemon wedges or slices, if desired.