Bake garlic with a sharp knife, slice off the top of the garlic heads to expose the cloves inside.
Drizzle small baking pan with some olive oil then place garlic heads inside, exposed side up.
Sprinkle the garlic heads with a little salt and pepper.
Slightly drizzle with olive oil, cover the pan with aluminum foil, then roast in the preheated oven for 40 minutes at 180°C.
Set aside to cool and prepare the dough; in a large mixing bowl or the bowl of your stand mixer fitted with a hook attachment, combine the yeast and warm water.
Stir it around and let sit for 5 minutes or until the yeast is foamy and dissolved.
Add flour, olive oil, salt, and sugar. Mix with the dough hook on low speed for 1 minute.
Once all of the ingredients are mixed, transfer dough onto floured surface and knead for 7 minutes.
Shape the dough into a ball and place in a large mixing bowl that has been coated lightly with olive oil.
Turn it over to coat all sides. Cover tightly with plastic wrap and allow to rise in a warm environment for 90 minutes.
Punch the dough down to release the air then divide the dough into two.
Roll each half into a ball and let rest in two separate bowls lightly covered for 10 minutes.
Preheat oven to 180°C and line two baking trays with parchment paper.
Remove garlic from the peel and chop; combine with the melted butter in a small bowl. Set aside.
Roll each ball of dough out into a 0.5cm-thick rectangle on a lightly floured surface..
Top each dough rectangle with melted butter/roasted garlic mixture then spinkle with parmesan.
Using a very sharp knife or pizza cutter, cut rectangles into long strips about 3 cm in width. Then, twist each strip up and top with a little more parmesan cheese if desired; transfer onto baking trays.
Bake breadsticks for 16-17 minutes
Sprinkle with half of cheddar cheese then return to the oven for about 4-5 more minutes.
Repeat with second batch and remaining cheese then bake for 4-5 minutes more; set on wire rack to cool slightly before serving.