In the bowl of a stand mixer, combine yeast, warm water, and 1 tsp of the sugar. Stir until the yeast dissolves and allow to rest/proof for 10 minutes.
After the yeast has rested and proofed, add the remaining sugar, 1 1/2 cups of flour, vegetable oil and salt. Mix to combine.
Add the remaining 1 1/2 cups of flour and, using the dough hook attachment, knead mixture for 7 minutes until the dough is smooth and elastic. It should pull away from the sides of the bowl. It will be slightly sticky. If it's too sticky, add the remaining 1/4 cup of flour.
Place dough in a large, well greased bowl. Cover with a kitchen towel or plastic wrap. Let it rest in a warm place (I use the microwave) for 1 - 1 1/2 hours or until it has doubled. If it's a cool day, place a bowl of water on the bottom rack of your oven and preheat the oven to 200. Once it's preheated, turn it off and place your bowl with the dough in it inside to rise.
Once dough has risen, punch it down and separate into 12 parts. Roll each part into a 9" rope. Place ropes on a parchment paper lined baking sheet. Cover and let rise again, for 1 hour.
Spray breadsticks with cooking spray and bake at 425 degrees for 10-12 minutes.
While the breadsticks are baking, melt your butter and add garlic topping ingredients, mixing well. When the breadsticks are fresh from the oven, brush with the garlic mixture. Serve warm!
Notes
Don't have a stand mixer? No big deal, you can make these by hand as well :)