In a stand mixer fitted with a dough hook attachment add the water, yeast, brown sugar, salt, and 1 ½ cups of the flour.
Knead the dough on a low speed until all the flour is incorporated. Add more flour, ½ cup at a time until the dough clears the sides of the bowl. It should be between 3-4 cups. You will know when you have enough flour when the dough sticks to itself more than to the side of the bowl or to your fingers. Once the dough has enough flour, knead for 3-4 more minutes.
Remove the dough to your hand for a second while you grease the bowl with cooking spray. Return the dough to the bowl, cover with plastic wrap and let rise until nearly doubled in size, about 1 hour.
Line a rimmed baking sheet with parchment paper and preheat the oven to 400°F. Spread 2 tablespoons of the melted butter over the top of the parchment paper.
Once the dough has risen, lightly grease a counter and tip the dough onto it. Roll or pat the dough into a roughly 16-inch x 8-inch rectangle.
Cut the dough using a pizza cutter into 1-inch strips. Twist each dough strip a few times and place on the baking sheet. Continue rolling, placing them about ½-1 inch apart.
Use a pastry brush to brush the remaining 2 tablespoons of butter over the breadsticks and sprinkle with garlic salt.
Let the breadsticks rise for 20 minutes before baking.
Bake for about 14-16 minutes until the breadsticks are golden brown on top.
Remove from oven enjoy hot.