Arrange a rack in center of oven; preheat to 425°. Place a baking sheet on rack to preheat.
In a small bowl, combine ginger, garlic, chili crisp, honey, miso, vinegar, and 1 Tbsp. oil. In a large bowl, combine potatoes and shallots. Add half of miso mixture; season with salt. Toss until coated.
Carefully remove baking sheet from oven. Drizzle with remaining 1 tsp. oil. Arrange vegetables in an even layer on sheet.
Pat chicken dry; generously season both sides with salt and pepper. Transfer to a large bowl and add remaining miso mixture. Toss until coated. Arrange on sheet skin side up with potatoes in a single layer.
Bake, rotating sheet halfway through, until an instant-read thermometer inserted into thickest part of chicken registers 165° and potatoes are cooked through and starting to caramelize, 30 to 35 minutes.
Turn on broiler. Broiler, watching closely, until chicken skin is starting to brown, 2 to 3 minutes. Top with cilantro and chili crisp.
