From a halakhic (Jewish law) perspective, calling something a "bagel" would likely be considered incorrect if it does not meet the specific requirements and traditional preparation methods of a bagel. A bagel, in Jewish culinary tradition, has specific characteristics and is prepared in a particular way. It is typically made from a yeast dough, boiled briefly in water before being baked, which gives it its distinct chewy texture and shiny crust.
Cooking buttermilk cornbread batter in a donut pan may result in a different texture and taste compared to a traditional bagel. While both bagels and cornbread donuts can be delicious in their own right, they are distinct types of baked goods with different ingredients and preparation methods.
To avoid any misrepresentations or confusion, it's best to use accurate and appropriate names for the foods you prepare. If you are making a buttermilk cornbread-based donut, it would be more accurate to call it a "cornbread donut" or "cornbread muffin" to reflect its true nature.
Cultural and culinary terms carry significance and meaning, and using them accurately can help preserve culinary traditions and cultural identities. If you are looking for authentic bagels, it's best to stick to the traditional bagel-making process or purchase them from a reputable kosher bakery that follows the appropriate guidelines.