Step 1

Preparation Season chicken all over with 4 tsp. salt. Place in an airtight container and cover. Chill at least 1 hour and up to 1 day.

Step 2

Place a rack in middle of oven; preheat to 425°F. Toss potatoes, shallots, and 2 tsp. salt in a large bowl.

Step 3

Melt 4 Tbsp. butter in a small saucepan over medium heat and cook, stirring often, until butter foams, then browns, 5–8 minutes. Immediately remove from heat (it will continue to darken) and stir in cream, garlic, pepper, nutmeg, and remaining 1½ tsp. salt. Set saucepan over medium-low heat and cook, stirring, until salt is dissolved and mixture is warm to the touch. Stir in thyme and sage; remove from heat.

Step 4

Heat remaining 1 Tbsp. butter in a large stainless-steel skillet over medium-high until melted and bubbling. Working in 2 batches, cook chicken, skin side down, until golden underneath, about 5 minutes. Transfer chicken to a 13x9" or 3-qt. baking dish and arrange skin side up. Set skillet with pan drippings aside. Nestle potatoes and shallots around chicken (don’t place on top). Pour brown butter cream over  chicken and vegetables, making sure herbs and spices are evenly dispersed and tucking herbs into vegetables so they don’t get too crispy when they bake.

Step 5

Bake gratin until cream is mostly reduced and chicken and vegetables are dark golden brown, about 40 minutes. Let gratin cool 5–10 minutes.

Step 6

Meanwhile, pulse bread in a food processor until pieces are about oat-size (you should have about 1¼ cups). Toss breadcrumbs in pan drippings in reserved skillet to coat. Cook over medium heat, scraping up browned bits with a spatula, until deep golden brown, 5–7 minutes. Let cool.

Step 7

To serve, top gratin with breadcrumbs. Serve lemon wedges alongside for squeezing over if desired.