Make the anchovy aioli: In a medium bowl, using a spoon, mash the garlic, salt, and anchovy to a paste. Whisk in the vinegar, then the mayonnaise. Gradually whisk in the oil.
Make the sandwiches: Arrange two of the slices of toast on a work surface and spread each with 1 tablespoon of the aioli. Arrange the roasted peppers, followed by the turkey and half of the arugula, on top of the aioli. Arrange two more slices of toast on a work surface and spread each with 1 tablespoon of the aioli. Top with the bacon and remaining arugula. Place them on top of the first slices. Spread each of the two remaining slices of toast with 1 tablespoon of the aioli. Place, face down, on the sandwich and press lightly to compact. Poke two skewers in each sandwich, cut them in half down the middle, and serve.