Preheat the oven to 375°F (190°C).
- In a medium bowl, whisk together eggs, heavy cream (or milk), salt, and pepper until smooth and fully combined.
- Heat olive oil in a 10-inch oven-safe skillet over medium heat. Add halved tomatoes and cook for 2-3 minutes, stirring occasionally, until softened. Remove from heat.
- Pour the egg mixture over the sautéed tomatoes in the skillet. Stir gently to distribute the tomatoes evenly in the eggs. Top with mozzarella and basil.
- Transfer the skillet to the oven and bake for 15-20 minutes, or until the eggs are set and lightly golden on top.
- Remove from the oven and let it cool slightly before slicing. Drizzle with balsamic glaze and garnish with fresh basil. Serve immediately.