Bake coconut in a shallow pan at 350°, stirring occasionally, 10 minutes or until toasted.
Whisk together sugar, egg yolks, and milk in a heavy saucepan over medium heat; cook, whisking constantly, 20 minutes or until mixture thickens and will coat a spoon (do not boil).
Remove from heat; whisk in toasted coconut, half-and-half, cream of coconut, and vanilla. Fold in banana. Cover and chill 3 hours.
Pour mixture into freezer container of a 1-gallon hand-turned or electric ice-cream freezer. Freeze according to manufacturer's instructions.
Pack freezer with additional ice and rock salt, and let stand 1 hour before serving. Garnish, if desired.
Note: For testing purposes only, we used Coco Lopez Cream of Coconut.