Prepare the artichokes: Fill a saucepan with water; squeeze in the lemon juice. Add the squeezed lemon halves to the water and season with salt.
Cut off and discard the top one-quarter of each artichoke with a serrated knife. Snap off the tough outer leaves. Peel the stem and base with a paring knife. Halve the artichokes lengthwise and drop into the saucepan. Cover and bring to a boil, then uncover, reduce the heat and simmer 5 minutes. Remove from the heat and let the artichokes sit in the hot liquid until just tender, 5 to 10 minutes; drain.
Whisk the olive oil, both vinegars, the sugar, herbs, garlic and tomato juice in a bowl. Put the artichokes and bell peppers in another bowl; drizzle with the vinegar mixture and let marinate 10 to 20 minutes.
Preheat a grill or grill pan to medium high. Grill the artichokes and peppers, turning, until browned, about 8 minutes. (Or, roast on a rimmed baking sheet in a 400 degrees F oven, 10 to 15 minutes.)
Assemble the platter: Arrange the cheeses, cured meats, tapenade, artichokes and bell peppers on a board or platter. Serve with the bread.
Photograph by Lisa Shin
Recipe courtesy Robert Irvine for Food Network Magazine