Combine the water and espresso powder in a large measuring cup. Whisk to dissolve. Set aside to cool. Pour into 2 ice cube trays. Freeze until solid, at least 8 hours. Transfer the ice cubes to a resealable plastic bag and store in the freezer for up to 3 days.

Combine the half-and-half and white chocolate in a small bowl. Place over a small pan of barely simmering water. Stir until the chocolate has melted and the mixture is smooth, about 5 minutes. Cool the chocolate mixture, whisking occasionally. Scrape the chocolate mixture into a blender. Add the vodka, sugar, vanilla and espresso ice cubes. Blend until smooth, at least 1 minute.

Pour into 4 large martini glasses. Garnish with grated white chocolate, if using, and serve.