For the pigs in blankets: Combine 1/3 cup warm water (110 to 115 degrees F) and the brown sugar in a medium bowl. Sprinkle the yeast over the water, and let stand until foamy, about 10 minutes. Whisk together the flour, cornmeal, Cajun seasoning and 1/2 teaspoon kosher salt in a small bowl. Add the flour mixture and the butter to the yeast, and mix with a fork until a dough forms.
Turn the dough out onto a flour-dusted surface, and knead by hand until smooth, about 5 minutes, using more flour as needed. Coat the inside of a medium bowl with cooking spray; add the dough to the bowl, and cover. Let the dough rise in a warm spot until doubled in size, 1 to 1 1/2 hours.
Preheat the oven to 400 degrees F. Coat a baking sheet with cooking spray. Make a slit down the length of each andouille link, cutting about halfway through, and stuff each with 1 tablespoon shredded cheese.
Turn the dough out onto a lightly floured surface. Roll into an 8-by-18-inch rectangle, about 1/8 inch thick. Cut lengthwise into 8 strips. Discard the 2 outer strips with the most uneven edges.
Wrap a strip of dough around an andouille link, coiling the strip from 1 end of the link to the other, leaving a 1/4-inch space between dough turns and leaving the ends of the sausage slightly exposed. Set on the prepared baking sheet, and repeat with the remaining dough and andouille. Brush the tops and sides with the beaten egg. Bake until golden brown, 18 to 22 minutes.
For the remoulade sauce: Meanwhile, stir together the mayonnaise, cornichons, mustard, ketchup, scallions and hot sauce in a small bowl. Refrigerate until ready to serve.
To serve: Cut each pig in a blanket into 4 pieces with a serrated knife. Serve with the remoulade sauce on the side.
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