New York strip steaks, each 280 to 340 grams and 2.5 centimeters thick, trimmed of nearly all fat around the perimeter
In a small saucepan over medium-high heat on the stove, bring the glaze ingredients to a boil. Reduce the heat and simmer until the glaze is reduced by about half, 3 to 5 minutes, watching carefully that it does not boil and burn. Remove from the heat and let cool and thicken slightly. Discard the garlic.
Combine the rub ingredients, and then season the steaks evenly with the rub. (Do not brush the steaks with oil.) Allow the steaks to stand at room temperature for 15 to 30 minutes before cooking.
Set the cooking grate aside; you will not be using it for this recipe. Make sure that the bottom vent on the grill is open. Place a chimney starter on the charcoal grate, and pack and fill it over the brim with all-natural lump charcoal (do not use briquettes). You need enough charcoal that, when ashed over, it will fill two-thirds of the charcoal grate. Place newspaper or paraffin cubes underneath the chimney starter (do not use lighter fluid), ignite it, and let the charcoal burn until lightly covered with white ash. Wearing insulated barbecue mitts or gloves, turn the coals out onto the charcoal grate. Break apart the larger pieces of charcoal to create a relatively even bed of coals. Using a sheet pan, fan any loose ashes from the coals.
Place the steaks directly on the coals. Put the lid on the grill, open the top vent on the lid, and cook until the steaks are browned and have reached your desired doneness, 6 to 7 minutes for medium rare, turning once and using a spatula to knock off any coals that may cling to the meat. Remove from the grill and let rest for 5 minutes. Just before serving, season the steaks with salt and drizzle with the glaze. Serve right away.