This is a BLT with class and sophistication — a topping of olive tapenade and homemade oregano dressing lends an Italian twist to the venerated classic sandwich. Don't let its decidedly upmarket ingredients fool you; this is no dainty sandwich and as such should be approached with a hearty appetite.
In a large bowl, whisk together the red-wine vinegar, mayonnaise, and Dijon mustard. Slowly whisk in the olive oil and canola oil until the sauce is thick. Add the oregano and season with salt and pepper, to taste.
Preheat a grill on high heat.
Coat the tuna with the oil and season with salt and pepper, to taste. Grill until seared on both sides but the center remains bright red (do not cook all the way through), about 1 minute per side.
On the bottom slices for each sandwich, layer the ingredients as follows: mayonnaise, bacon, onion, tomato, egg, tuna, basil, arugula, and avocado. Drizzle each sandwich with 1 teaspoon of the oregano dressing (reserve the rest for other uses such as salad) and pecorino. Place some tapenade on the top slice and place on top of the sandwich.