Scrape black gills out of mushrooms with a spoon and remove stem.
Brush outsides (tops) of mushroom caps lightly with olive oil. Place mushrooms on a parchment paper lined baking sheet, gill side up; sprinkle with ¼ teaspoon salt and ¼ teaspoon pepper.
In a small bowl, mix together ricotta, tomatoes, mozzarella, Parmesan, basil, and ⅛ teaspoon black pepper. Fill mushroom caps with cheese mixture.
In a small skillet over medium heat, melt butter. Add garlic, stirring constantly for one minute. Remove from heat. Stir in panko, parsley, oregano, and salt until combined.
Spread panko mixture evenly over cheese filling.
Bake mushrooms in the preheated oven until tender and cheese is melted, about 15-17 minutes.
Prep-Ahead: Mix up the filling and prepare the breadcrumb topping the night before. Refrigerate both until you're ready to stuff the mushrooms. Plan to add a few minutes to the baking time.
Storage & Reheating Suggestions: Refrigerate leftovers up to three days, tightly wrapped. To reheat, put the mushrooms on a baking sheet and into a preheated oven (400°F) for ten minutes or until heated through.