Preheat oven to 375°F. Heat olive oil in medium sauté pan over medium-high heat. In small bowl, beat 4 eggs and the milk with whisk until well blended. Add egg mixture to pan, and scramble until cooked through. Season with salt and pepper. Set aside.
Place cooking parchment paper on large cookie sheet; sprinkle with brown rice flour. Roll or press out dough on cookie sheet to about 10-inch square. Sprinkle 1/2 cup of the cheese down the center, leaving 1 inch at each end. Spoon on eggs and bacon, and top with remaining cheese.
Use sharp knife to make even slits, about 1 inch wide, down both sides. Fold over both ends. Starting with one end, carefully bring side pieces in and overlap them as in braiding. Alternate each side over the other until you finish all sides and have a nice tight braid. Brush braid with egg wash all over.
Bake 20 to 24 minutes or until golden brown.
Cool 5 minutes. Slice and eat while warm.