Cook the beef: Sauté the diced onion for 3-5 minutes. Add the ground beef and cook until browned. Mix in taco seasoning and green chiles. Once cooked, melt the shredded Colby Jack cheese into the beef.
Toast the bread: Butter one side of each slice of Texas toast and place butter-side down on the griddle. While toasting, butter the top side. Flip and grill until both sides are golden and crispy.
Assemble: Place American cheese on 4 slices of toast, then add the cheesy beef mixture. Top with the remaining slices of toast.
Grill the sandwiches: Press lightly and grill each side for 1-2 minutes until the cheese is fully melted.