In the bowl of an electric mixer fitted with a dough hook, combine the yeast, milk, sugar, and butter, and mix well for 2 minutes. Add the egg, and mix well. Add 4 cups of the flour, the cornmeal and salt. Beat at low speed until all the flour is incorporated, then on medium speed until a ball of dough forms, adding more flour as needed if too sticky.
Remove from the mixer, form into a ball, and place in a lightly oiled bowl. Cover and let rise in a warm place until nearly doubled, about 1 hour.
Turn out the dough onto a lightly floured surface and pat into a thick rectangle, about 1-inch thick. Roll out until about 1/4-inch thick, and with a sharp knife, cut the dough into squares, about 2 1/2 to 3 inch-square.
Heat the fryer to 360 degrees F.
Drop the dough into the hot oil, being careful not to overcrowd the sopapillas as they are cooking, and turning them constantly to cook on all sides until golden, about 3 minutes per batch. Remove the sopapillas from the oil with a slotted spoon and drain on paper towels.
Serve the sopapillas hot, drizzled with honey.
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