In a small saucepan over low heat, combine the maple syrup, bourbon, and cinnamon stick (if using). Warm gently for 5-7 minutes, stirring occasionally. Do not boil. Remove from heat, stir in the 1 tbsp of butter until melted, and set aside. Keep warm.
In a large skillet over medium heat, cook the chopped bacon until crispy, about 6-8 minutes. Transfer to a paper towel-lined plate. Drain most of the bacon fat from the skillet. In a bowl, whisk the 6 eggs with milk, salt, and pepper. Melt 1 tbsp butter in the same skillet over medium-low heat. Pour in the eggs and cook, gently folding with a spatula, until just set but still soft, about 3-4 minutes. Fold in the cooked bacon and 2 tbsp of chives. Transfer to a bowl and cover to keep warm.
Take two slices of bread. Using a small sharp knife, cut a deep pocket into the side of one slice, being careful not to cut through the other three sides. Repeat with all bread slices to make 4 pocket slices. Spoon the scrambled egg and bacon mixture evenly into the 4 pockets, pressing gently to fill. Use your finger to dab a little water along the edges of the pocket opening, then dust lightly with flour. Press the edges firmly to seal.
In a shallow dish, whisk together the 3 eggs, milk, vanilla, cinnamon, and salt for the egg wash. Heat 2 tbsp of butter in a large skillet or griddle over medium heat. Dip each stuffed bread pocket into the egg wash, letting it soak for 10-15 seconds per side. Place in the hot skillet. Fry for 3-4 minutes per side, until deeply golden brown and crispy, adding more butter as needed. Work in batches to avoid overcrowding.
Stack two stuffed toast pockets on each white plate. Drizzle generously with the warm bourbon maple syrup. Garnish with additional chopped fresh chives. Serve immediately.