Combine the yeast, sugar, and 2 tablespoons of the vegetable oil in the bowl of a stand mixer fitted with a dough hook. Add the warm water. With the mixer on low speed, beat the mixture for about 1 minute to dissolve the yeast. If the yeast mixture doesn’t begin to foam after a few minutes, it means it’s not active and you will have to start over with fresher yeast.
In a large mixing bowl, combine the flour and 1 teaspoon of the salt. Add it 1/4 cup at a time to the yeast mixture, mixing on low speed until the dough lightly comes together. Increase the speed to medium and beat until the dough pulls away from the sides of the bowl, forms a ball, and starts to climb up the dough hook.
Coat a large bowl with the remaining 1 teaspoon vegetable oil. Put the dough in the bowl and turn it to oil all sides. Cover the bowl with plastic wrap, set aside in a warm, draft-free place, and let rise until doubled in size, about 1 hour.
Meanwhile, in a large skillet, melt the butter over medium heat. Add the onion, bell pepper, the remaining 1 1/2 teaspoons salt, and the cayenne. Cook, stirring, for 4 minutes. Add the crawfish and cook, stirring, for 5 minutes until they are soft. Remove from the heat, drain off any excess liquid from the pan, and set aside to cool.
Remove the dough from the bowl and turn it onto a lightly floured work surface. Push it down, then, using your hands, pat it out to flatten it. Pick it up, dust the work surface with flour, and return the dough to the work surface. Roll it out to a 20 X 15-inch rectangle, about 1/8 inch thick.
Combine the cheeses in a medium-size mixing bowl. Sprinkle half of the cheese over the upper half of the rectangle of dough, leaving a 1/2-inch border. Spoon the crawfish mixture evenly over the cheese. Top with the remaining cheese. Fold the other half of the dough up over the filling, forming a half-moon shape, and pinch the edges tightly to seal completely. Fold the edges over, seal securely, and then crimp. Carefully transfer the dough to a baking sheet lined with parchment paper. With a sharp, pointed knife, make three slits on top, about 6 inches apart. Brush the surface of the dough with the beaten egg and sprinkle with the kosher salt and black pepper. Cover with plastic wrap and set aside in a warm, draft-free place until doubled in size, about 1 hour.
Preheat the oven to 400°F.
Remove the plastic wrap and bake the bread until golden brown, 30 to 35 minutes. Let cool slightly. Cut crosswise into 12 equal portions and serve warm.
Yield: 1 large loaf, 12 servings