Butter crunch French bread topping
Does your bread look like this (photo)? From your comments, it seems that you think your bakery's "butter crunch French bread" may be the same bread which is called "Dutch crunch," among other names. Since no one else is answering this question, I'll take a stab at it even though I have never baked any of this bread, &amp; tasted it for the first time just now.

In my supermarket, they call it "Dutch crust," and the topping's ingredients are called out separately: Rice Flour, Palm Shortening, Sugar, Active Dry Yeast.  

Semifreddi's Bakery website   http://www.semifreddis.com/products   lists all the bread's ingredients:  Enriched Flour (wheat flour, malted barley flour, niacin, reduced iron, thiamine mononitrate, riboflavin, folic acid), Water, Safflower and/or Sunflower and/or Expeller Pressed Canola Oil, Sugar, Rice Flour, Sea Salt, and Yeast.

Wikipedia describes Dutch crunch bread as having sesame oil and rice flour in the topping, although neither of my examples mention the sesame oil, just the rice flour... But no cheese in any I see. Any cheesy topping is probably not the same as what I am thinking of.