Make the dressing: Mince and mash the garlic with the salt until the mixture forms a paste. In a small bowl stir together the lime juice, the soy sauce, the sugar, the garlic paste, the chilies, and the mint until the sugar is dissolved and let the dressing stand at room temperature for 30 minutes to develop the flavors.
Sprinkle both sides of the steak generously with the pepper, rubbing the pepper into the meat, and brush them with some of the oil. Grill the steak, seasoned with salt, on a well-oiled rack set 4 to 5 inches over glowing coals, turning it once, for 16 to 18 minutes, or until it is springy to the touch for medium-rare meat. (Alternatively, the steak may be cooked in the same manner in a well-seasoned ridged grill pan, brushed with the oil and heated over moderately high heat until the begins to smoke.) Transfer the steak to a cutting board and let it stand for 15 minutes.
While the steak is grilling, in a skillet heat 1/2-inch of the oil over moderately high heat until it is hot but not smoking and in it fry the shallot, stirring, for 30 seconds to 1 minute, or until it is golden. Transfer the shallot with a slotted spoon to paper towels and let it drain. The shallot may be cooked 1 day in advance and kept covered and chilled.
Cut the steak across the grain into 1/4-inch-thick slices and divide the slices among 4 plates, overlapping them in the center. Surround the steak with the green beans, top the green beans with the bean sprouts, and sprinkle the bean sprouts with the shallot. Spoon 2 tablespoons of the dressing over each serving of steak and serve the remaining dressing separately.