Preparation Season chicken on all sides with 2 1/2 tsp. salt and place in a large bowl. Add ginger beer, garlic, 3/4 cup vinegar, and 3 Tbsp. ginger to bowl and toss to combine. Cover and chill at least 2 hours and up to 24 hours. Meanwhile, whisk miso, 3/4 cup oil, 1 tsp. salt, and remaining 6 Tbsp. vinegar and 1 tsp. ginger in a small bowl. Mix in scallions. Let dressing sit at room temperature up to 1 hour, or chill up to 24 hours. Prepare a grill for high heat; brush grate lightly with oil. Grill chicken, turning occasionally, until lightly charred and an instant-read thermometer inserted into thickest part of thigh registers 165°F, 12–15 minutes. Transfer to a platter and tent with foil to keep warm. Toss radishes with remaining 1 Tbsp. oil in a medium bowl; season lightly with salt and pepper. Grill, turning occasionally, until charred in spots, 8–10 minutes. Transfer to platter with chicken. Toss lettuce with about one-third of dressing in a large bowl. Drizzle another third of the dressing over grilled radishes. Serve remaining dressing alongside.