Combine the oil, thyme, and crushed garlic in a small bowl. I often prepare this the day before though it is not necessary.
For the sauce, combine the mayo, mustard and dill in a bowl.
Brush the portbello caps with the oil mixture and place on heated grill stem side up. Flip after approx 4 minutes and let grill on other side for an additional 3 - 5 minutes. The mushrooms should begin to crisp around the edges.
The rest is pretty straight forward.