The bottom half of this rustic roll was scooped out to make room for the vegetables and cheese; the black-olive paste adds a tangy finish.
Heat broiler to medium high. Slice 2 lemons in half, and squeeze juice into bowl of cold water. Add lemon halves to bowl.
Trim tips and outer leaves from artichokes; slice thinly, lengthwise; submerge in lemon water. Combine olives with 1 tablespoon oil.
Heat 1 1/2 tablespoons oil in skillet over medium heat; add garlic. Saute until fragrant, about 30 seconds. Pat artichokes dry; add to skillet. Saute until golden, about 5 minutes. Squeeze juice of remaining lemon over artichokes; season with generous pinch of salt and pepper, and add 1/2 cup chopped parsley; toss. Transfer to small bowl; cover with foil.
Return skillet to heat; add remaining 1 1/2 tablespoons oil. Arrange tomatoes in skillet. Adjust seasoning; sprinkle with remaining 1/2 cup parsley. Cook until golden around edges, about 5 minutes. Turn; saute 1 to 2 minutes.
Slice open rolls; scoop out bottom, creating cavity for filling; spread with olive mixture. Mound artichokes over olives; arrange several tomatoes over artichokes. Arrange cheese over tomatoes. Place sandwiches and tops of rolls, crumb side up, on baking sheet; broil until cheese is melted and bread is golden, about 2 minutes. Close sandwiches.