Begin by making the basil mayonnaise so the flavors have time to come together. Combine all the ingredients in a blender and pulse until combined. Cover and refrigerate while you prepare the sandwich.
Heat a cast iron griddle pan/skillet or outdoor grill until smoking hot. Season the skirt steak with plenty of kosher salt and freshly ground black pepper. Drizzle with extra-virgin olive oil then grill both sides for 3 to 4 minutes until medium rare. Set aside loosely tented with aluminium foil while you prepare the other fillings.
To assemble, take one slice of the toasted bread and rub a garlic clove all over 1 side. Put a big slather of basil mayonnaise across the bread. Layer the lettuce over the top and then the thick-cut slices of tomato. Top with the crispy bacon slices and season with kosher salt and freshly ground black pepper. Take the skirt steak and using a sharp knife cut across the grain into thick slices. Lay the pieces of the sliced skirt steak on the top of the open sandwich and serve with more basil mayonnaise on the side.