Prepare the marinade: In a large bowl, whisk together buttermilk, egg, hot sauce, ranch dressing, kosher salt, and freshly ground black pepper until well combined. Submerge chicken thighs in the mixture, fully coating them. Cover and refrigerate for at least 30 minutes or up to 1 day, or proceed immediately to frying if desired.
Mix the dredge: In a shallow dish, combine all-purpose flour, smoked paprika, kosher salt, and black pepper. Stir to mix evenly. Set aside.
Make the slaw: In a medium bowl, toss together shredded iceberg lettuce, chopped chives, pickle juice, kosher salt, and pepper to taste.
Heat oil: In a large cast iron skillet or Dutch oven, heat vegetable oil over medium-high heat until it reaches 350°F.
Coat the chicken: Remove chicken from the marinade one at a time, letting excess liquid drip off. Dredge each piece in the seasoned flour, pressing flour onto the surface to build a thick crust. Place coated chicken on a plate and repeat with remaining pieces. For extra crispiness, dredge each piece in the flour once more before frying.
Fry the chicken: Carefully add the double-coated chicken to the hot oil. Fry for 10 to 15 minutes, turning as needed, until golden brown and cooked through.
Drain: Remove chicken from oil and drain on paper towels to remove excess oil.
Assemble the sandwiches: Spread ranch dressing on the bottom half of each toasted and buttered brioche bun. Layer with pickles, fried chicken, and a generous helping of chive and iceberg slaw. Add additional ranch dressing to the top bun if desired.