Remove the stems from the portobello caps and wipe each one clean with a damp paper towel. Arrange them facing up in a shallow baking dish then set aside.

In a small bowl, whisk together the balsamic vinegar, oil, tamari, oregano, and a pinch of salt & pepper. Pour the marinade on each of the mushroom caps and use your fingers to spread it out to the sides and bottom. Allow to sit for about 10 minutes.

Meanwhile make the aioli by combining the mayo, lemon zest and juice, basil and garlic in a blender. Blend on high until smooth. Add one to teaspoons of water if needed to thin. Taste test and add salt as desired.

Lightly grease a grill pan or cast iron skillet then warm over medium heat. Add the mushroom caps and cook for 5-7 minutes on each side, until tender. Serve warm with basil aioli and enjoy!