In a medium bowl, whisk hoisin sauce, soy sauce, garlic, rice vinegar, honey, five-spice powder, salt, and red pepper flakes. Remove ¼ cup marinade; cover and refrigerate until ready to use.

Add chicken to remaining marinade and toss to coat. Cover and let sit at least 30 minutes at room temperature or up to 24 hours in the refrigerator.

Prepare a grill for medium-high heat; preheat 5 minutes. Lightly brush grates with oil.

Remove chicken from marinade and grill, turning once and brushing with reserved ¼ cup marinade, until cooked through and an instant-read thermometer inserted into thickest part registers 165°, 8 to 10 minutes (these thighs are very forgiving; you can continue to grill until more fat renders and thermometer registers 175° to 180°, if desired).

Make Ahead: Chicken can be grilled 3 days ahead. Store in an airtight container and chill.

Place carrot and radish in a fine-mesh strainer. Sprinkle with salt and 2 teaspoons granulated sugar and gently massage into vegetables until softened, about 3 minutes. Transfer to a medium heatproof bowl.

In a small pot over medium-high heat, heat water, vinegar, and remaining ½ cup granulated sugar, stirring, until sugar is dissolved and mixture is steaming, 1 to 2 minutes. Pour hot pickling liquid over vegetables and stir to coat. Cover and let sit at least 1 hour.

Make Ahead: Pickles can be made 2 weeks ahead. Fully submerge vegetables in brine in an airtight container and chill.

Spread 1 tablespoon mayo on bottom of each sandwich roll; season with salt.

Top each with a piece of warm char siu chicken, a handful of Vietnamese pickles, cilantro, and chiles. Close with top bun.