Boudin Blanc–Stuffed Turkey Breasts with Chestnuts

Turkey and brine:
1/2 cup kosher salt
1/4 cup sugar
1/4 cup sweet white wine (optional)
2 skin-on, boneless turkey breasts (about 4 pounds total)
Boudin blanc:
2 tablespoons coarse fresh breadcrumbs
1/2 cup heavy cream
1 cup low-sodium chicken broth
1/2 cup roasted chestnuts from a jar
1 tablespoon Cognac or brandy
2 bay leaves
1 teaspoon kosher salt, plus more
1 teaspoon yellow mustard seeds
3/4 teaspoons coriander seeds
1 whole allspice
1 whole clove
3/4 teaspoons white peppercorns
1 pound ground pork belly or 3/4 pound ground pork and 1/4 pound finely chopped bacon
1 tablespoon finely chopped fresh thyme
1/8 teaspoon ground mace
1/8 teaspoon ground nutmeg
Assembly:
1/4 cup (1/2 stick) unsalted butter
2 cups roasted chestnuts from a jar
4 sprigs thyme
Kosher salt, freshly ground pepper
Ingredient info: Roasted chestnuts can be found at specialty foods stores and some supermarkets.

For turkey and brine:
Bring salt, sugar, and 2 quarts water to a boil in a large pot, stirring to dissolve salt and sugar. Let cool, then add wine, if using. Place turkey and brine in a large resealable plastic bag. Seal bag and chill 10–12 hours.
Remove turkey from brine and pat dry
Let sit at room temperature 1 hour.
For boudin blanc:
Soak breadcrumbs in cream in a small bowl 20 minutes.
Meanwhile, bring broth, chestnuts, Cognac, bay leaves, and a pinch of salt to a low simmer in a small saucepan. Cook until chestnuts are very soft but not falling apart and liquid is reduced by half, 12–15 minutes. Discard bay leaves; chill while preparing spices.
Toast mustard seeds, coriander, allspice, and clove in a small skillet over medium heat until fragrant and mustard seeds begin to pop, about 4 minutes; let cool. Finely grind toasted spices and peppercorns in spice mill or with mortar and pestle.
Mix pork, thyme, mace, nutmeg, spice mixture, breadcrumb mixture, and 1 teaspoon salt in a large bowl. Coarsely chop chestnuts and add to pork mixture, along with cooled cooking liquid. Stir pork mixture to combine.
DO AHEAD: Boudin blanc can be made 2 days ahead. Wrap tightly and chill.
For assembly:
Preheat oven to 400°F. Working 1 at a time, place turkey breast on cutting board, skin side up. Holding knife parallel to work surface, cut through breast, stopping about 1/2" before you get all the way through. Open breast like a book and mound boudin blanc down center, leaving a 1" border. Fold bottom half of breast over filling, then fold top half over so it slightly overlaps. Tie at 1" intervals with kitchen twine.
Place turkey breasts on a rack set inside a roasting pan. Add 1 cup water and roast until skin is golden brown and an instant read thermometer inserted into the center of stuffing registers 145°F (breast meat should register 160°F), 1–1 1/2 hours. Let rest 10 minutes before slicing.
Meanwhile, heat butter in a medium skillet over medium-high heat. Add chestnuts and thyme sprigs and cook, stirring often, until chestnuts are soft, 5–7 minutes; season with salt and pepper. Serve turkey with chestnuts.