To make garlic oil, simmer 2 cloves of garlic in 3-4 Tbs of canola oil over low heat for 40 minutes. Remove cloves, cool, then measure out the needed oil.
In a double boiler over barely simmering water, heat garlic oil. Add cheese and stir until melted; the oil will separate. Remove from heat, but let stand over the hot water.
Mix together flour, salt, and yeast in the bowl of a stand mixer fitted with the dough hook attachment, running the mixer on low for about 1 minute.
With the mixer still on low, slowly add water, followed by melted cheese.
Mix and knead on low for 30 minutes, stopping as needed to scrape dough off the hook or the sides of the mixing bowl.
Turn out onto a lightly-floured work surface, stretch and fold the dough over, and place in a lightly oiled bowl. Cover and let stand 15 minutes.
Place the dough on a lightly-floured surface and shape into a block 4" x 5" x 1". Place on a baking sheet lined with parchment, cover, and refrigerate 3 to 4 hours, or overnight.
Roll out dough into a rectangle 15" x 9" x 1/4" thick. Cover and return to refrigerator for 1 hour.
Trim rectangle to 14 x 7 1/2 inches, retaining scraps to bake as a chef's snack. Cover and refrigerate for 1 hour.
Cut dough into breadsticks 3/8 of an inch wide and place 1/4 inch apart on lined baking sheets. Cover and let proof for 60 to 90 minutes or until a depression remains when pressed lightly with a finger.
Place a baking stone on the middle rack and preheat the oven to 325°F.
Set one baking sheet at a time on the baking stone, and bake for 22 to 24 minutes, rotating the sheet halfway through, or until the breadsticks are a golden brown.
Remove an let cool completely on the baking sheet.