In 1-quart saucepan, heat simple syrup ingredients over low heat until sugar is dissolved.
Let stand 15 minutes.
Cover; refrigerate 2 hours until chilled.
Strain syrup; discard solids.
In small bowl, stir together 2 tablespoons sugar and ½ teaspoon gingerroot.
Place mixture on small flat plate.
Rub fresh gingerroot slice around rims of 2 martini glasses to moisten.
Dip moistened rims of glasses in ginger-sugar mixture.
Refrigerate until ready to use.
Fill cocktail shaker or small pitcher with ice.
Add gin, pomegranate juice and 2 tablespoons of the Ginger Simple Syrup.
(Cover and refrigerate remaining simple syrup for another use. )
Shake or stir to blend and chill.
Pour into prepared glasses, straining out ice.
Add prosecco.
Garnish with pomegranate seeds.
Notes / Tips / Wine Advice:
Make-Ahead Magic
You can make the ginger syrup up to one month in advance. Cover and refrigerate until ready to use. The extra-cold syrup will make the cocktail nice and frosty.