Trim the artichoke leaves and stems and blanch in salted, boiling water with a little of the lemon juice. Use only enough water to cover. When tender remove from the water, cool, and clean. Save the leaves for another use. Discard the hairy choke and save the hearts and stem for the dish. Slice into 1/8-inch slices.
In a saute pan over high heat, add 1 tablespoon olive oil and saute the fennel in it until tender. Add salt and pepper, to taste, remove and keep warm.
Wipe out the saute pan and add in the peanut oil and bring to medium high heat. Salt and pepper the fillets and brown on 1 side about 5 minutes. Turn and saute 2 more minutes and remove from the pan. Add the sliced garlic and 1/2 of the remaining olive oil and cook 2 minutes. Add the sliced artichokes and saute until starting to brown. Add the tomatoes, white wine, stock, lemon zest and juice, and remaining olive oil and reduce the liquid by 1/4.
Return the fish to the mixture, add the capers and basil, and check salt and pepper. Cook 2 more minutes until fish is just flaky and check salt and pepper. Divide the fennel among 6 warm dinner plates and top with the fillets. Sauce with the vegetable mixture and serve.