In a small bowl, mix together chiles, lime juice, and fish sauce; set aside.
Place palm sugar and 3/4 cups water in a medium saucepan; place over high heat and bring to a boil. Reduce heat and cook until mixture is a dark caramel color and reaches 310 degrees on a candy thermometer, about 15 minutes. Stir in chile mixture until dissolved. Remove from heat and stir in cilantro and miso, if using; add additional fish sauce and lime juice, if desired. Set caramel mixture aside.
Preheat oven to 425 degrees. Line a baking sheet with parchment paper and set aside.
Place brussels sprouts in a large bowl and toss with olive oil and salt to combine. Place brussels sprouts cut-side down on prepared baking sheet. Transfer to oven and bake until leaves are dark brown, 8 to 10 minutes.
Transfer brussels sprouts to a large bowl. Add 1/3 cup caramel mixture and toss to coat. Transfer to a serving dish; serve immediately.