In the bowl of a stand mixer fitted with a dough hook, combine the water, yeast, sugar, salt, and 1 cup of flour. Mix on medium speed to blend. (If you don’t have a stand mixer, this is also easy to mix by hand in a large bowl.)
Continue adding flour just until the dough clears the sides of the bowl. You should add at least 3 cups flour total, but not more than 4. The dough should be soft and slightly sticky, but not leave much residue on your fingers. Continue kneading for 2-3 minutes, until dough comes together into a ball. Let it rest in the bowl for 10 minutes.
Preheat the oven to 400 degrees F. Pour melted butter onto a large, rimmed baking sheet, and use a pastry brush (or your fingers) to spread it out across the entire surface area. Set the baking sheet aside.
Turn out the dough onto a lightly floured work surface. Using your hands or a rolling pin, work the dough into a long rectangle, approximately 16” by 7”. Using a pizza cutter, cut the dough into strips about 1” wide.
Lift each strip, fold in half, twist it slightly, and place about 1/2” apart on the buttered baking sheet. Sprinkle the breadsticks lightly with Italian seasoning, garlic powder, and sea salt.
Let the breadsticks rise at room temperature for about 20 minutes, then bake for 15-17 minutes, until the tops are golden. Remove and serve right away.