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1
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.
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2
Add the egg, and mix well.
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3
Add 4 cups of the flour, the cornmeal and salt.
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4
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.
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5
Remove from the mixer, form into a ball, and place in a lightly oiled bowl.
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6
Cover and let rise in a warm place until nearly doubled, about 1 hour.
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7
Turn out the dough onto a lightly floured surface and pat into a thick rectangle, about 1-inch thick.
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8
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.
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9
Heat the fryer to 360 degrees F.
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10
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.
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11
Remove the sopapillas from the oil with a slotted spoon and drain on paper towels.
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12
Serve the sopapillas hot, drizzled with honey.