Preheat the oven to 350°F and line a large enough baking sheet with parchment paper.
Cut a V-shaped section from the top of the bread loaf, this works best with a serrated bread knife. Remove the cut-out bread to form a "boat". The hole should be large enough to hold the filling. Scoop out more bread if needed but stop 1/2-inch from the bottom of the bread.
Place the bread on the prepared baking sheet.
Whisk together the eggs, sour cream, salt, pepper, and chives.
Evenly distribute the crumbled feta cheese and cherry tomatoes in the bread loaf.
Pour the egg mixture into the bread loaf. Work slowly so that the filling has time to sink in and doesn't overflow.
Brush the crust of the bread with oil or melted butter.
Bake for 30 minutes, or until light golden brown on top and the egg does not "jiggle" when you shake the baguette.
Serve warm and enjoy!