Stir together sugar and water in a saucepan over medium-high heat until sugar is dissolved. Add strawberries and bring to a boil; boil for 10 minutes. Reduce heat to medium-low and simmer until consistency is syrupy, about 10 minutes.

Strain liquid through a fine-mesh sieve into a resealable jar, pressing solids to extract liquid; chill.

Dip a coupe glass rim into a shallow saucer of water. Spread decorating sugar on a separate small, shallow plate. Dip glass rim into sugar to coat.

Pour vodka, amaretto, and 1/2 fluid ounce strawberry simple syrup into a cocktail shaker half-filled with ice. Cover and shake until very cold. Strain into the prepared glass. Top with Champagne, then add ice cream. Garnish with strawberry.