Preheat oven to 400 degrees F. Set out a rimmed baking sheet and two 8-ounce oven-proof oval ramekins.

Set a medium-sized skillet over medium heat. Add 1 tablespoon olive oil and when hot, about half the zucchini (zucchini won't cook well if overcrowded, so it's best to sauté in batches); sprinkle with a pinch of sea salt. Cook until each side is a rich golden brown, about 3 minutes per side. Repeat for remaining zucchini.

Divide zucchini in half, and tuck and fold cooked zucchini all along the edges and bottom of the ramekins. Drizzle a tablespoon of Tabasco Green Sauce over each ramekin, and add 2 eggs to each. Sprinkle eggs with sea salt. Set ramekins on a rimmed baking sheet and carefully slide into oven.

Bake 9 minutes, remove from oven, and divide mozzarella cubes between each dish, tucking cubes all around the eggs. Slide back into oven and cook just until egg whites are set, 3 - 6 minutes more.

Remove from oven, top with black pepper to taste, and serve right away. (Ramekins will be very hot – set on a heat resistant surface and use caution.)