Bring water to a boil in a saucepan. Stir in sugar, butter, and salt; cook until sugar dissolved. Reduce heat to low; whisk in 1 cup cornmeal until smooth. Stir in remaining 1/2 cup cornmeal to make a very thick, workable dough.

Heat 3 cups vegetable oil in a deep fryer or large saucepan to 350 degrees F (175 degrees C).

Meanwhile, grease your hands well with 2 teaspoons vegetable oil. Scoop about 3 tablespoons cornmeal dough; roll into a ball, then shape into a 3-inch long stick about 1/2-inch wide. Repeat with remaining dough, oiling your hands as needed.

Deep fry cornmeal sticks, working in batches of 3 or 4 at a time, until golden brown. Drain on paper towels and keep warm.

Whisk mayonnaise, ketchup, and garlic salt together in a bowl until well combined. Serve cornmeal sticks with dipping sauce.