Gently wash the tomatoes well, using your hands to 'scrub' away and dirt or debris. Dry them with a paper towels.
Using a pairing knife, carefully cut a circular plug out of the top center of each tomato. Use a sturdy spoon to gently hollow out the seeds and pulp within.
Place the prepped tomato 'bowls' onto the wells of a tin muffin pan. The tomatoes will sit on top of the wells, and the juices that leak out during cooking will collect within preventing any mess in the oven.
Drizzle the olive oil evenly out over top of the tomatoes. Season them with salt & freshly cracked black pepper, to taste.
Bake the tomatoes at 400° for 8-10 minutes.
Remove the hot pan and gently crack an egg into the center of each of the tomatoes, careful not to break the yolks and then discard the shells.
Return the filled tomatoes to the oven, and continue baking them an additional 12-15 minutes. When the eggs are cooked to your desired preference, remove them from the oven.
Season the stuffed tomatoes with salt & pepper again, to taste.
Carefully transfer the hot tomatoes to serving plates, top with fresh chives & a sprinkle of shredded Parmesan cheese, and enjoy!