Nestle the artichokes in the tomato sauce, pesto side up.
Bring to a boil and then reduce to a simmer for about 60 minutes.
Turn artichokes every 10-15 minutes to keep rotating them in the sauce.
Artichokes are ready when they're fork tender.
Remove artichokes from the sauce, tenting with foil, and reduce the tomato sauce for 10-15 minutes over medium heat, until thickened.
Place artichokes in serving dish, top with sauce and remaining pesto. Serve hot.
To make ahead: prepare according to the instructions until the artichokes are fork tender. To reheat, bring to a simmer and until the artichokes are hot. Remove the artichokes, tent with foil and reduce the sauce according to the instructions. Serve hot with the reduced tomato sauce and pesto.