Melt butter in large skillet; add garlic and cook 1 to 2 minutes. Remove butter from heat and lightly brush butter over both sides of the Texas toast. Reserve the remaining butter in the skillet to cook the eggs.
Grill steaks over direct medium heat for 5 to 7 minutes, until browned. Turn, brush with barbeque sauce and continue grilling 2 to 3 minutes until steaks are desired doneness.
Remove steaks to cutting board to rest at least 5 minutes. Toast bread over direct high heat for 1 to 2 minutes until browned, turning once. Lightly brush one side of toast with any remaining barbeque sauce.
Heat butter over medium high heat. Crack each egg individually into skillet. Cook 2 to 3 minutes until white is just starting to set; flip. Continue cooking 1 minute until egg whites are set. Season eggs as desired.
Thinly slice each steak and place on Texas toast. Top with tomatoes, blue cheese and fried egg.
It’s not a barbeque sandwich without the Weber® Smoky & Thick Hickory BBQ Sauce.