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