In the bowl of an electric stand mixer fitted with the dough hook, combine all ingredients for dough except flour. On low speed, gradually add flour until a soft, smooth dough is formed. Increase speed to medium and knead dough for 7 minutes, or until smooth and elastic. Keep in mind you may not use the full 3 cups flour or you may need a bit more. Judge the dough by the texture instead of by an exact amount of flour. It should pull away form the sides of the bowl and form a soft, smooth ball of dough that doesn't stick to your fingers.
Remove dough to a lightly oiled bowl and cover with beeswax wrap or a clean kitchen towel. Let rise in a warm place until doubled in size, about 1 1/2 hours.
Lightly flour a clean countertop and roll the dough into about an 8X18-inch rectangle. Brush the melted butter evenly across the dough.
In a small bowl, combine the granulated sugar and cinnamon. Sprinkle this mixture across the dough and lightly press into the top of the dough.
Using a pizza cutter or sharp knife, cut the dough into 12 equal sticks, about 1-inch wide. As you pick up each breadstick, twist it a few times and place them on a parchment lined baking sheet about 1/2-inch apart.
Preheat oven to 375°F. Bake for about 15 minutes, or until golden brown.
Whisk together the powdered sugar, milk, and vanilla until a pourable mixture forms, adding more or milk if needed.
Let the breadsticks cool for about five minutes before drizzling with the glaze. Serve warm.