Whisk together the balsamic vinegar, olive oil, and ginger together in a bowl until well combined.

Place the portobello mushrooms in a zip lock bag (or casserole dish or tupperware container) and pour the balsamic-ginger marinade over them. Spoon the marinade over the mushrooms so that the whole mushroom is coated. Sprinkle both sides of each mushroom with salt, black pepper, and Italian seasoning or Herbs de Provence. Allow mushrooms to marinate 10 to 20 minutes, spooning the marinade over them periodically.

Preheat the grill to medium-high. Place mushrooms gill-side up on the grill and pour any remaining marinade over the gills of each mushroom. Sprinkle with salt and pepper and cover the grill. Cook until mushrooms are very juicy and grill marks appear, about 5 to 8 minutes.

Use tongs to carefully flip the mushrooms (Note: the juices will spill over the grill and may cause it to flame up, so be very cautious when flipping). Cook an additional 5 to 8 minutes, until mushrooms are soft on the inside and crispy on the outside.

Transfer mushrooms to a cutting board, slice into ¼-inch thick slices and serve immediately.