Halve each sourdough roll horizontally, leaving one long side attached. Scoop out some of the soft bread in the top half of the roll, leaving crust intact.
Drain artichokes, reserving 4 tablespoons marinade. Trim off and discard any tough leaves or tips. Cut in half lengthwise and set aside. Brush reserved marinade over scooped-out portion of each roll.
Spread the Rondele equally over the bottom half of each roll. Top the cheese with equal portions of arugula, red pepper strips, artichokes, gouda, onion, and cucumber. Bring the top portion of the roll over the vegetables to close the sandwich.
Nutritional analysis per sandwich.