Cut the potatoes in half, then quarters, then eighths. Add them to a large bowl and cover with ice water. Let soak for at least 1 hour.

In a small mixing bowl, combine the Mesquite seasoning, thyme, garlic powder and pepper.

Generously brush both sides of the steak(s) with butter. Generously rub the seasoning on all sides of the steak. Leave the steak on the counter to warm close to room temperature.

Meanwhile, clean, oil and preheat the grill to about 300 degrees F.

Remove the potatoes from the ice water and pat them dry with a towel. Be sure and remove all the moisture.

Place the potatoes on the indirect side of the grill and shut the lid. Let the potatoes smoke for about 8 to 10 minutes.

In a Dutch oven or fryer, add enough oil to deep fry and heat to 325 degrees F.

In a small bowl, combine the corn flour and cornstarch.

Remove the potatoes from the grill and place them on a sheet pan. Brush the potatoes lightly with the remaining butter, then toss them in the corn flour mixture and shake off any excess.

Fry the potatoes for about 2 to 3 minutes. Drain and place on a wire rack to completely cool.

Heat the oil to 375 degrees F. and fry the potatoes again for about 2 minutes, or until golden brown. Season with Original seasoning or salt and pepper and Parmesan cheese, if using.

Place steak(s) on the indirect side of the grill, shut the lid and cook for about 6 to 8 minutes.

Place the steaks over the direct heat and grill for about 3 to 4 minutes on each side, or until the internal temperature is 115 to 120 degrees F. Let rest a few minutes before cutting against the grain. Serve warm with steak fries.