Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
Using a serrated knife, cut a long rectangle out of the top of each baguette, removing the inner bread to create a cavity while leaving the bottom and sides intact.
In a medium mixing bowl, whisk the eggs and heavy cream until the mixture is uniform in color.
Fold in the shredded cheddar cheese, cooked protein, chopped chives, salt, and black pepper.
Place the hollowed baguettes onto the prepared baking sheet and divide the egg mixture evenly among the cavities.
Bake for 20 to 25 minutes, or until the egg filling is puffed and set, and the bread is golden brown.
Remove from the oven and let stand for 5 minutes before slicing into sections for serving.