Stir water, yeast, and sugar together in a small bowl or liquid measuring cup. Set aside to foam up.
Meanwhile, melt the butter and measure out the flour and salt into the bowl of a stand mixer. Stir with the dough hook for a few seconds to disperse the salt into the flour. Pour in the foamy yeast mixture and start to incorporate. Drizzle in half of the melted butter. Scrape the sides if necessary and knead 7 minutes. Dough should be sticky. If it's dry, you've added too much flour, so add in a few sprinkles of water to get it to come together as a stickier dough. You're aiming to get the dough stuck to the bottom of the bowl. If you touch it with your fingers after 7 minutes, than maybe a small piece or two will stick. Grease the bowl and dough well with oil and let rise 30-45 minutes in a warm place until doubled in size.
Punch down dough and roll out to be 2 ft x 1 ft, approximately, on a floured board. Cut into 1/2-3/4 inch strips using a pizza cutter. Twist two strips together to create breadsticks and place onto baking sheet lined with parchment paper or silicone baking mat. You may have to cut them to fit on the baking sheet. Let rise another 30 minutes or so. They should be almost touching by now.
Preheat oven to 425 degrees. Drizzle remaining melted butter over breadsticks, sprinkle with garlic salt and cheeses and bake 8-10 minutes or until poofy, hot, bubbly and brown. Cool 3-5 minutes before tearing apart and snarfing down.