Preheat a grill pan over medium-high heat.
Drizzle mushroom caps with EVOO and place on the grill pan, gill side down, for about 3 minutes.
Flip caps and season with salt and freshly ground black pepper. Spread a spoonful or so of roasted red pepper paste over the mushroom cap in a thin layer.
Top with a slice of smoked mozzarella cheese and tent with foil to melt.