How to Make It
Preheat oven to 275°F. Beat egg whites with a stand mixer fitted with the whisk attachment on medium speed until soft peaks form, 3 to 4 minutes. (To test for soft-peak stage, stop the mixer, and lift up the whisk; whites should peak and droop.) With mixer running on medium speed, gradually add 1/2 cup sugar, 1 tablespoon at a time, beating for 20 seconds after each addition. Increase mixer to high speed; beat 30 to 45 seconds. Meringue should be slightly glossy, white, and somewhat stiff. Remove meringue from mixer; fold in cranberry sauce until mostly smooth.
Shape meringue mixture into 8 large ovals (about 2/3 cup each), using a large spoon to press and smooth mixture against a second large spoon. Gently arrange meringues on a baking sheet lined with parchment paper.
Bake meringues in preheated oven until outsides are set and very slightly browned, 10 to 15 minutes. Remove from oven; let cool on baking sheet 10 minutes.
Ladle about 1/3 cup nutmeg anglaise into each of 8 shallow serving bowls. Using a spatula, gently remove meringues from baking sheet; place 1 meringue in middle of each bowl. Set bowls aside.
Stir together 1 cup water and remaining 2 cups sugar in a small saucepan. Using a pastry brush dipped in water, brush off any sugar clinging to sides of pan. Bring mixture to a boil over high, taking care not to jostle pan. Boil, undisturbed, until syrup starts to turn slightly pale brown, about 12 minutes. Gently swirl pan to even caramelization. Cook caramel, swirling pan occasionally, until golden brown, 13 to 18 minutes.
Remove caramel from heat; let cool in pan, stirring occasionally, until caramel thickens and no longer runs off a spoon like water, 2 to 5 minutes. (Caramel should be thick and viscous but still thin enough to fall off the spoon.)
Place 2 mugs or cups about 2 feet apart on a work surface covered with parchment paper (to make cleanup easier later). Dip tines of a fork into caramel in pan, and lift fork straight up so that the dripping caramel starts to fall back into the pan. Before all the caramel drips back in, use a quick, sharp flinging wrist motion to flick the fork back and forth about 2 feet above parchment paper between the 2 mugs. The caramel will attach to the mugs and create strings of spun sugar in between. Keep dipping the fork in caramel and flicking it back and forth across the mugs to create strands of spun sugar. The spun sugar will fall and gather on top of the parchment paper. After 5 or 6 rounds of dipping and flicking caramel, you should have enough strands to gather together and shape with your hands into a small (5-inch) oval of spun sugar; this will be the garnish for 1 dessert. Repeat process to create spun-sugar garnishes for remaining 7 servings. Place 1 spun-sugar garnish on each meringue.
Stir together cranberry slices and sugar in a small bowl; let stand 5 minutes. Arrange cranberries evenly over anglaise in bowls. Serve immediately.