I was at a bar a while ago and ordered a variety of appetizers. One was what must have been a grilled portobello mushroom that was served with a smoky mayo sauce. Last month I got around to trying to recreate it. Easy and delicious. What I did was to:
1) coat with Olive Oil, 4 portobello mushrooms
2) grill mushrooms on a hot grill (can be done in a broiler or even a hot oven) until they started to shrink (on the grill they get nice grill marks...). When finished, cut into strips or cubes.
3) mix several tablespoons of Kewpie Mayonnaise (a delicious Japanese mayo, you can use any mayo) with liquid smoke to taste. I've recently discovered that it's not always possible to buy liquid smoke. I probably ended up using a teaspoon or so of it to about 4 Tbs of the mayo...but you should do this to taste.
4) drizzle the smoky mayo over the strips or cubes of portobellos.