Whisk together coconut milk, curry powder, minced garlic, grated ginger, salt, and sugar in a large bowl. Add chicken thighs, coat evenly, cover, and refrigerate for at least 1 hour or overnight.

Combine rice flour, salt, and black pepper in a shallow dish. Remove chicken from marinade, letting excess drip off. Dredge each piece firmly in the flour mixture. For extra crunch, dip briefly back in the marinade and dredge again.

Heat 2 inches of oil in a deep skillet over medium-high heat to 350 degrees F (175 degrees C). Use a thermometer to maintain temperature throughout frying.

Carefully lower chicken thighs into the hot oil. Fry for 5 to 7 minutes per side until deep golden brown and the internal temperature reaches 165 degrees F (74 degrees C). Work in batches. Transfer to a wire rack to drain.

Whisk together Thai chili sauce and mayonnaise until smooth. Toast brioche buns in a dry skillet or under the broiler for 1 to 2 minutes until golden.

Spread Thai chili mayo on both sides of each toasted bun. Layer on crispy chicken, cucumber slices, pickled carrots, cilantro, and Thai basil. Press gently and serve immediately.