Whisk the flour, salt, pepper, and garlic salt together in a large bowl until evenly combined.
Pour about 1/2 cup of the buttermilk into the seasoned flour and mix until a slightly shaggy batter forms; repeat as needed to create a batter that clings to the chicken but is not too thin.
Dip each chicken tender into the remaining buttermilk, then coat with the seasoned flour batter; place the breaded tenders on a wire rack and let them rest briefly to set the coating.
Discard any leftover buttermilk. Heat oil in a deep fryer or large heavy pot to 350°F (175°C).
Fry 3–4 breaded tenders at a time, careful not to overcrowd, until golden brown and cooked through, about 3–5 minutes per batch depending on thickness; transfer to a wire rack set over a baking sheet to drain.
Butter both sides of each Texas toast slice. Toast the bread on a skillet or griddle over medium heat until golden brown on both sides.
Assemble sandwiches by placing three chicken strips on four slices of toasted Texas toast, topping each with two slices of Monterey Jack cheese, and spreading about 1 tablespoon honey barbecue sauce on one slice before closing.