Remove the stems from the portabellos. In a small bowl, mix ¼ cup balsamic vinegar and ¼ cup olive oil. Place the mushrooms on a baking sheet. Using a brush. the front and back of each mushroom with the marinade. Sprinkle with kosher salt and pepper, and let sit for 15 minutes.
Place the mushrooms on grill (or in a grill pan) and cook about 5 minutes per side, until juicy. In the last minute, place provolone cheese slices on top of each mushroom and grill until melted, then remove from the grill. Brush the cibatta rolls with olive oil and place them on the grill until toasted.
Slice the tomato, and de-strem the arugula.
Place each grilled portabello cap on half of a roll. Top with a spoonful of pesto, a tomato slice, a handful of arugula, and the other half of the roll.