For the black bean relish: Combine the onions, cilantro, olive oil, tomatoes, beans, chiles and lime juice in a bowl and season with salt and black pepper. Let the relish sit at room temperature for 30 minutes to allow the flavors to meld.
For the hollandaise: Place the lime juice and yolks in a medium stainless-steel bowl set over a pot of simmering water. Whisk the yolks until pale yellow and fluffy. Slowly add the melted butter, a few tablespoons at a time, and whisk until thickened. Remove from the heat, whisk in the steak sauce and season with the salt and black pepper. Keep warm.
For the Texas toast: Heat a grill pan over medium-high heat. Combine the garlic, butter and some salt and black pepper in a small bowl. Butter both sides of the bread with some of the garlic butter, and grill until nicely charred on both sides.
For the steak: Put each slice of steak in between pieces of plastic wrap and use a meat mallet to pound them into thin steaks. Sprinkle both sides with some of the steak rub and some salt and black pepper. Heat the oil in a cast-iron pan over high heat. Add the steaks and cook until a crust forms, about 1 minute. Flip and cook for another minute until the other side forms a crust as well.
For the poached eggs: Bring 3 cups water and the vinegar to a gentle simmer in a large high-sided frying pan. Break each egg into a cup and gently add to the water. Poach until the yolks are nearly set, 4 to 5 minutes. Remove the eggs from the pan with a slotted spoon to drain the liquid. Season the top with salt and black pepper.
For assembly: Spoon some of the black bean relish on top of each piece of the Texas toast. Top each with 2 pieces of steak, a poached egg, then some of the hollandaise. Garnish with whole cilantro leaves.