Remove the stems from the mushrooms and discard. Wipe the mushroom caps clean with a damp cloth.
In a small bowl, combine olive oil, balsamic vinegar, salt, pepper and red pepper flakes. Brush mushroom caps with mixture.
Preheat a grill pan over medium heat. When the rim of the pan is hot to the touch, place the mushrooms in the pan with the cap side down. Sear until grill marks appear, about 4 - 5 minutes.
Turn mushrooms a quarter turn and sear an additional 3 - 4 minutes. When sear marks have appeared, turn the mushrooms over and repeat the process.