Taiwanese Turkey Rice

1 (4-lb.) skin-on, bone-in turkey breast or 3 lb. shredded leftover cooked turkey
1 Tbsp. plus 1½ tsp. kosher salt (optional)
5 scallions, trimmed, halved (optional)
1 (2") piece ginger, peeled, sliced ¼" thick (optional)
8 whole star anise (optional)
¼ cup turkey stock or low-sodium chicken broth (optional)
Sauce:
½ cup high-quality lard, turkey fat, duck fat, or goose fat
16 shallots (about 12 oz.), shaved on a mandoline or very thinly sliced
1 head of garlic, finely chopped
¼ cup michiu (Taiwanese rice wine) or sake
¼ cup light soy sauce
¼ cup sugar
2 tsp. freshly ground white pepper, plus more
3 cups low-sodium chicken broth (optional)
Cooked white rice (for serving)

Turkey:

If using a raw turkey breast, sprinkle turkey all over with salt; place on a wire rack set inside a rimmed baking sheet and chill, uncovered, at least 6 hours and up to 1 day. (This will result in tender, flavorful meat.)
Place turkey, scallions, ginger, and star anise in a stockpot. Pour in water to cover turkey by 1". Bring to a boil, then reduce heat and simmer, skimming foam from surface as needed, until an instant-read thermometer inserted into thickest part of breast registers 150°F, about 75 minutes. Transfer turkey to a cutting board and let sit until cool enough to handle (internal temperature should rise to 165°F while the turkey cools).
Strain stock through a fine-mesh sieve into a large heatproof bowl; discard solids. Pour 3 cups stock into a large heatproof measuring glass and set aside for sauce; reserve remaining stock for another use.
Shred turkey with a fork or your hands, removing and discarding skin (or shred along with meat if you prefer).
If starting with leftover turkey: Preheat oven to 350°F. Spread turkey in an even layer on a rimmed baking sheet, drizzle stock over, and cover tightly with foil. Cook until warmed through, about 15 minutes.
Sauce:

Heat lard in a medium saucepan over medium-low. Add shallots (it will not look like enough fat at first) and cook, stirring often, until softened into a single layer, then continue to cook, stirring occasionally, until golden brown, 20–25 minutes total. (Shallots will crisp as they cool.)
Drain shallots in a fine-mesh sieve set over a heatproof bowl. Transfer shallots to paper towels to drain; set aside. (You don’t need to salt them.) Heat shallot fat in a medium saucepan over medium. Add garlic and cook, stirring often, until fragrant and just starting to color, about 3 minutes. Add michiu, soy sauce, sugar, 2 tsp. white pepper, and reserved 3 cups stock (if you are using leftover turkey, use chicken broth instead). Bring to a boil, then reduce heat and simmer, stirring occasionally, until sauce is reduced by half and glossy, about 25 minutes. Taste and add up to 2½ tsp. more white pepper if desired.
To serve, divide rice among shallow bowls and pile shredded turkey over. Spoon 2–3 Tbsp. sauce over each bowl and top with reserved fried shallots.