Step 1

Season chicken on all sides with 2 1/2 tsp. salt and place in a large bowl.

Step 2

Add ginger beer, garlic, 3/4 cup vinegar, and 3 Tbsp. ginger to bowl and toss to combine.

Step 3

Cover and chill at least 2 hours and up to 24 hours.

Step 4

Meanwhile, whisk miso, 3/4 cup oil, 1 tsp. salt, and remaining 6 Tbsp. vinegar and 1 tsp. ginger in a small bowl.

Step 5

Mix in scallions.

Step 6

Let dressing sit at room temperature up to 1 hour, or chill up to 24 hours.

Step 7

Prepare a grill for high heat; brush grate lightly with oil.

Step 8

Grill chicken, turning occasionally, until lightly charred and an instant-read thermometer inserted into thickest part of thigh registers 165°F, 12–15 minutes.

Step 9

Transfer to a platter and tent with foil to keep warm.

Step 10

Toss radishes with remaining 1 Tbsp. oil in a medium bowl; season lightly with salt and pepper.

Step 11

Grill, turning occasionally, until charred in spots, 8–10 minutes.

Step 12

Transfer to platter with chicken.

Step 13

Toss lettuce with about one-third of dressing in a large bowl.

Step 14

Drizzle another third of the dressing over grilled radishes.

Step 15

Serve remaining dressing alongside.