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Place chicken breasts in a resealable freezer bag; using a meat mallet or rolling pin, pound them to an even ¼-inch thickness. Cut each pounded breast in half.

Pour water into a medium bowl; add salt and sugar and whisk until dissolved. Place chicken breasts in brine, cover, and refrigerate for at least 4 hours or overnight.

Line a plate with paper towels. Pour oil into a large pot until it reaches a depth of about 1 inch. Heat over medium-high heat until shimmering (about 350°F).

Whisk egg and milk in a medium bowl. Whisk flour, cornstarch, baking powder, garlic powder, pepper, Accent (if using), and remaining salt in another bowl.

Drizzle 4 tablespoons egg mixture into flour mixture and mix with a fork until clumpy.

Remove chicken from brine and pat dry. Dip each breast into egg mixture, then into flour mixture, pressing firmly.

Carefully place chicken into hot oil without crowding. Cook, turning, until golden brown and crispy, 4 to 5 minutes total. Place on paper towels to drain.

Whisk mayonnaise, barbecue sauce, and mustard in a small bowl.

Spread sauce on top and bottom buns. Top each bottom bun with chicken and pickles. Close sandwiches and serve immediately.