Preheat the oven to 350 degrees and grease a 9x13 baking dish.
Heat the oil in a skillet over medium heat. Add the tempeh bacon and cook until crispy (approx. 3-5 minutes). Remove from the skillet and set aside.
Add the vegan eggs, milk, mustard & dry seasonings to a bowl and whisk to combine.
Layer 1/2 of the croissants, tempeh & cheese in the prepared baking dish and then repeat the layer with the remaining ingredients. Pour over the egg mixture and gently press the croissants down. Place in the oven for 40-45 minutes, or until the croissants are golden and the vegan eggs are set (see notes).
Remove from the oven and allow to sit for 5 minutes to set. Top with chives and serve.