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Slice the chicken breasts in half lengthwise and horizontally, making two thinner fillets out of each breast. You can do this by placing your hand flat on top of the chicken breast, holding a sharp knife parallel to your cutting board, and slicing the chicken in half. If necessary, pound the chicken lightly with the flat side of a meat mallet until they are flat and even in thickness.
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Combine the buttermilk, parsley, chives, salt and freshly ground black pepper. Marinate the chicken in the buttermilk mixture for at least 4 hours to overnight.
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To make the herbed sandwich spread, whisk together the mayonnaise, buttermilk, Dijon mustard, chopped parsley and chives in a small bowl. Season to taste with salt and freshly ground black pepper. Chill until ready to use.
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Heat a grill/griddle or large skillet over medium-high heat. Cook the bacon until crispy and remove it from the griddle or pan. Drain away most of the bacon grease.
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Remove the chicken breasts from the marinade and place them directly onto the hot grill/griddle or pan without letting the marinade drip off the chicken. Discard the remaining marinade. Cook the chicken breast for about 4 to 5 minutes on each side until browned and cooked through. Cooking time will vary depending on how thick your chicken slices are. Transfer the chicken to a plate and cover with foil. Wipe down the griddle or pan.
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Build the sandwiches by spreading butter on one side of each slice of bread. Flip the slices over and spread the herbed sandwich spread on the other side of all four slices. Layer a slice of Swiss cheese, the chicken breast, 2 tomato slices, 2 slices cooked bacon and another slice of Swiss cheese on top of 2 slices of bread. Top with the remaining two slices of bread, leaving the buttered side up.
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Pre-heat the grill/griddle or skillet to medium heat. Place the sandwich on the heated cooking surface and grill for about 5 to 7 minutes, weighing the sandwich down with a bacon press or heavy spatula. Flip the sandwich over and cook for another 5 minutes until the bread is golden brown and the cheese has melted.
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Transfer to a cutting board, slice in half and serve immediately.