Clean the portobello mushrooms by gently rubbing the cap and gills with a damp paper towel. Place the mushrooms cap side down in a large dish or alternatively a zip loc bag. In a bowl whisk together all of the ingredients for the marinade and once well combined, pour over the mushrooms. Leave them to marinate for approx 1 hour (up to 6 hours)
To make the pesto, in a blender or food processor combine all of the pesto ingredients and pulse until its blended into a smooth consistency. Taste and adjust seasoning accordingly and then place in the fridge until ready to serve.
Heat a grill pan or barbecue on medium heat (or a sandwich press would also work) and grill the portobello mushrooms for approximately 5 minutes per side until grill marks form and they become tender. Once grilled cut then into 1/2 inch thick slices, drizzle any of the leftover marinade over each mushroom and then serve with a spoonful of the pesto on top.