Preheat a gas grill to medium-high heat. Clean grates.
Prepare Portobello mushrooms by removing the stems. You can cut them with a knife. Using a spoon, scrape down the gills of each mushroom.
Season on both sides with salt, pepper and thyme (optional). Brush with olive oil.
Cut butter into 6 equal bits and add to the inner side of the mushrooms.
Place mushrooms on the grill, stem side up and grill for 5-7 minutes, until the liquid on top has almost evaporated. Flip and grill for 5-7 more minutes.
Drizzle with balsamic vinegar (optional) and serve.