Prepare the pears: In a large nonstick pan over medium heat, warm the butter. When it begins to foam, add the pears. Lower the heat slightly and cook, stirring gently to coat the pears in the butter. Add the sugar, salt, and vinegar. Cook until the pears are golden and tender but not mushy, 5 to 15 minutes depending on ripeness. Remove from the heat and set aside.

Make the sabayon: Fill a pot with an inch or two of water and bring to a simmer. Combine the egg yolks and sugar in a stainless-steel bowl. Whisk in the wine. Place the bowl over the pot, making sure the bowl does not touch the water. Turn the heat to low and whisk the egg constantly until the mixture becomes as thick as cake batter and no liquid remains in the bottom of the bowl, 3 to 8 minutes. Remove from the heat.

Pour about 1/4 cup sabayon in each rimmed dessert dish. Top with 4 pear wedges, garnish with almond slivers, pomegranate seeds, and chocolate shavings.