In a large bowl or heatproof pitcher, stir hot coffee, condensed milk, milk and vanilla. Cover and chill at least 8 hours or overnight.

Pour chilled mixture into a shallow pan (I used a 13-by-9-inch baking pan). Freeze until solid, about 4 hours.*

Meanwhile, make the whipped cream: Beat heavy cream and sugar on high speed until stiff peaks form, about 2 to 3 minutes. Chill until ready to use.

Toast the coconut: Heat oven to 350 degrees F. Spread coconut flakes on a baking sheet; toast in oven, stirring occasionally, until golden brown, about 7 to 10 minutes.

Scoop frozen coffee mixture into serving glasses; top with whipped cream and toasted coconut.

*Alternatively, you can freeze the coffee mixture in an ice cream maker. Here's how to do it.