Rub room temperature steak with oil and season with salt, pepper, granulated garlic and granulated onion. Preheat griddle over medium-high heat.
In a pot, cover eggs with water and bring to a rolling boil. Remove from heat, cover and let stand 10 minutes. Crack the eggshells and soak in cold water to loosen. Peel eggs and place yolks in bowl; chop the whites and reserve on cutting board. Mash the yolks with salt, pepper, grated onion, garlic, mayo, mustard, relish, hot sauce and Worcestershire. Taste to adjust seasoning; and stir in the whites.
Grill steak 8-10 minutes turning once. Let rest a few minutes then thinly slice on an angle against the grain.
Assemble sandwiches on toasted muffins or biscuits starting with chopped lettuce, tomato, red onion, a few slices of steak then top with deviled egg salad and set muffin or biscuit tops in place.