Braised Artichokes with Tomatoes and Mint

Place tomatoes in a large Dutch oven or other heavy pot, crushing with your hands; add wine, red pepper flakes, 2 tsp. salt, 1/2 cup oil, and 2 cups water; set aside.
Pulse anchovies and garlic in a food processor until finely chopped. Add mint and pulse until coarsely chopped. With the motor running, stream in remaining 1/2 cup oil; process until a coarse paste forms. Set pesto aside.
Remove several layers of dark-green outer leaves from artichokes (keep going until you get to the tender light-green leaves). Using a serrated knife, cut off top 1" of artichokes and trim stem ends. Rub cut ends with lemon halves to prevent browning. Working with 1 artichoke at a time, use a paring knife or vegetable peeler to remove tough outer green layer from base and stem to reveal pale-green underneath; rub all over with lemon. Halve through stem and rub cut sides with more lemon. Use a spoon to scoop out choke, then pull out spiky inner leaves; rub insides with lemon. Rub reserved pesto all over artichoke halves and place artichokes in a single layer inside reserved pot, submerging in tomato mixture.
Bring to a simmer over medium-low and cook, turning artichokes occasionally, until hearts are fork-tender, 55–65 minutes. Transfer artichokes to a platter and tent with foil to keep warm.
Increase heat to medium, bring sauce to a boil, and cook until slightly thickened, 10–15 minutes. Taste and season with more salt if needed. Spoon over artichokes.