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Using an electric mixer with a dough hook, whisk the yeast, sugar, and warm water together, for 2 minutes to dissolve the yeast. Add the onion mixture. Add the salt and flour. With the mixer on low, mix until the dough starts to come together. Increase the speed to medium-high and mix until the dough comes away from the sides of the bowl and crawls up to dough hook. Grease a mixing bowl with the vegetable oil. Place the dough in the greased bowl and turn once. Cover the bowl with plastic wrap and place in a warm, draft free place until the dough doubles in size about 1 1/2 hours.
Turn the dough out onto a baking sheet. Punch the dough and press the dough out to form the size of the pan. Place dough in pan and sprinkle with kosher salt. Cover the dough and allow to double in size, about 45 minutes.
Preheat the oven to 350 degrees F. Bake the dough for 30 to 35 minutes or until the dough is golden brown.
Slice the bread into 8 to 12 pieces, depending on desired size of the sandwich. Spread each side of roll with the aioli. Divide the roasted vegetables and cheese evenly between each sandwich.
Put the sandwiches on a baking sheet and bake in the oven until the sandwiches are hot and the cheese is melted, for about 5 to 8 minutes.