Cook the tempeh bacon.
In a large skillet over medium heat, add a splash of olive oil.
Arrange the tempeh slices in a single layer and cook for 3-4 minutes per side, until golden brown and crisp.
Set aside on a paper towel-lined plate.
Prepare the halloumi.
Pat the halloumi slices completely dry with a paper towel.
Heat a grill pan or the same skillet to high.
Sprinkle the halloumi on both sides with black pepper.
Sear the halloumi.
Place the halloumi on the hot pan and cook for 2-3 minutes per side, until golden-brown and grill marks appear.
Set aside.
Make the dressing.
In a medium bowl, whisk together the ½ cup olive oil, lemon juice, garlic, and salt and pepper to taste.
Add the arugula and toss well to coat.
Assemble the sandwiches.
Spread mayonnaise and tapenade on each slice of toasted bread. On six of the slices, layer the crisp tempeh, red onion, tomatoes, sliced egg, vegetarian Parmesan, and avocado.
Finish and serve.
Top the layered with the seared halloumi, fresh basil, and the dressed arugula.
Cover with the remaining slices of bread, cut in half, and serve immediately.
Pat the halloumi slices completely dry before searing to get a beautiful golden-brown crust and prevent sticking.