Preheat oven to 350 degrees F (175 degrees C). Spread 3 cups flaked coconut onto a baking sheet.
Bake coconut in the preheated oven, turning once, until toasted, 6 to 10 minutes. Cool completely.
Beat sugar and eggs together in a bowl until light and frothy; add cream of coconut and beat well. Add half-and-half and vanilla extract into egg mixture, beating well after each addition. Stir toasted coconut and flaked coconut into half-and-half mixture.
Pour coconut mixture into the bowl of an ice-cream maker. Pour milk into coconut mixture to fill machine to the fill-line, if necessary. Freeze according to the manufacturer’s instructions.