In a medium bowl, mix all the ingredients together. Refrigerate until ready to use. If possible, make a day or 2 ahead to give all the flavors time to meld together.
In a small bowl, whisk first 8 ingredients and set aside.
Attach a deep-fry thermometer to side of a heavy wide pot. Add enough oil to measure 2". Heat over medium heat to 350°.
Place shrimp and 2 tablespoons spice mix in a medium bowl and toss to coat.
Pour buttermilk into another medium bowl. In another medium bowl, whisk the flour and cornmeal.
Dip seasoned shrimp briefly in buttermilk, then coat with flour mixture. Give a gentle shake to remove any excess flour.
Working in batches, fry shrimp, stirring occasionally, until golden brown and just cooked through, about 4 minutes per batch.
Transfer to a plate lined with paper towels. The paper towels will absorb excess oil, because you definitely don't want the shrimp to taste greasy.
Open rolls and spread cut sides with rémoulade.
Top with lettuce, tomato, pickles, and shrimp.
Serve with hot sauce, for a little extra kick.