Preheat oven to 400°F.

Place mushroom caps, gill side up, on a rimmed baking sheet; drizzle with oil and vinegar, and season with salt and 1/4 teaspoon of pepper. Bake until caps are just tender, about 10 minutes.

Meanwhile, combine tomato, olives, breadcrumbs, cheese, and chives in a medium bowl. Season with the remaining 1/4 tsp of pepper.

Divide tomato mixture evenly (about 1/2 cup per mushroom) among portobello caps. Bake 10-12 minutes or until lightly browned and mushrooms are tender. Serve hot.