On a work surface, sprinkle the minced garlic with salt and, using the flat side of a knife, mash the garlic to a smooth paste. In a small bowl, whisk the garlic paste with the rosemary, paprika and olive oil. Rub the marinade all over the steak and let stand at room temperature for 2 hours or refrigerate for up to 2 days.
Heat a grill pan. Season the flank steak with salt and pepper and grill over moderately high heat, turning once, until medium-rare, about 7 minutes. Transfer the steak to a board and let rest for 5 minutes. Thinly slice the steak across the grain.
Grill the bread until crisp and golden, about 2 minutes per side. Spread each slice with 1/2 teaspoon each of the mayonnaise and mustard. Arrange the steak on the bread and top with the pickled green tomatoes.
In a medium bowl, toss the arugula with the tomato pickling liquid and season with salt and pepper. Mound the arugula on the sandwiches and serve.