In a large roasting pan, combine the diced tomatoes, white wine, vegetable stock, and olive oil. Season with salt and red pepper flakes. Set the pan aside.

For the pesto rub: Place the anchovies, garlic cloves, and basil leaves into a food processor. Pulse until combined.

With the motor running, slowly pour in the 1/2 cup olive oil until a thick, uniform paste forms.

Pull away the thick, dark green outer leaves of the artichoke until only the tender, pale green leaves remain.

Use a vegetable peeler to remove the tough skin from the bottom and the stem (leaving 3–4 inches of the stem attached).

Cut off the top third of the artichoke leaves.

Crucial: Rub every cut surface immediately with a lemon half to prevent browning.

Slice the artichoke in half lengthwise. Use a spoon to remove the fuzzy "choke" and any spiky inner leaves.

Place the trimmed halves into a bowl of cold water with lemon slices until all 4 artichokes are prepped.

Remove artichokes from the water and pat dry. Brush the anchovy pesto generously on both sides of each artichoke.

Place the artichokes cut-side down into the roasting pan with the tomato broth.

Bring the sauce to a boil on the stovetop over medium-high heat.

Reduce heat to medium-low, cover tightly with a lid or foil, and simmer "low and slow" for 45 to 60 minutes.

Turn the artichokes in the sauce several times during cooking to ensure they are well-coated. Cook until a fork easily pierces the heart.

If the sauce reduces too quickly, add a splash more stock.

Arrange the artichokes on a large platter. Spoon the concentrated pan juices over the top and serve warm.