How to Make It
Prepare the Bread Pudding Muffins: Preheat oven to 350°F. Melt butter in a large skillet over medium-high. Add apples and 1/2 teaspoon each of the salt and cinnamon. Cook, stirring often, until tender, 12 to 15 minutes.
Whisk together cream, milk, sugar, egg yolks, eggs, vanilla, and remaining 1/2 teaspoon each salt and cinnamon in a large bowl. Stir in apple mixture and chopped doughnuts. Let stand until liquid is absorbed, about 10 minutes.
Divide mixture evenly among 12 jumbo muffin cups coated with cooking spray. Bake in preheated oven until a knife inserted in center comes out clean, about 25 minutes, rotating pans on rack after 15 minutes.
Prepare the White Chocolate Sauce: Bring cream to a simmer in a small saucepan over medium. (Do not let cream come to a boil.) Remove from heat, and stir in chocolate. Let stand 1 minute. Stir until mixture is smooth.
Prepare the Raspberry Sauce: Bring raspberries, sugar, and lemon juice to a boil in a large saucepan over medium. Cook, stirring and pressing down on berries occasionally, until berries break down and mixture is syrupy, about 10 minutes. Pour mixture through a fine wire-mesh strainer into a bowl; discard solids. Return syrup to saucepan; bring to a boil over medium-high. Cook, stirring occasionally, until syrup thickens to a honey-like consistency, about 12 minutes. Remove from heat. If desired, stir in liqueur. Serve muffins drizzled with sauces.