Bring the water and sugar to the boil in a saucepan over high heat until the sugar dissolves and the syrup turns clear. Pour into a double boiler along with the cream and milk. Whisk until the syrup has dissolved into the milk, then whisk in the egg yolks and instant coffee until completely incorporated.
Set the double boiler insert over (but not touching) a pan of gently simmering water. Cook, stirring constantly until the custard has thickened and will stick to the back of a spoon, about 10 minutes. Pour through a mesh sieve into a bowl and stir in the coffee grounds. Refrigerate several hours until cold.
Pour into an ice cream maker and freeze according to manufacturer's instructions.