In a large saucepan, combine the first four ingredients. Cook over medium heat for 10 minutes or until sugar is dissolved. Remove from the heat. In a bowl, beat the eggs and yolks. Stir 1 cup hot cream mixture into eggs; return all to the pan, stirring constantly. Cook and stir until slightly thickened and a thermometer reads 160°. Cool. Refrigerate overnight.
In a bowl, beat whipping cream and extracts until stiff peaks form. Fold into egg mixture with coconut. Fill cylinder of ice cream freezer two-thirds full; freeze according to manufacturer's directions. Refrigerate remaining mixture until ready to freeze. Transfer to a 4-qt. freezer container; freeze for at least 4 hours before serving.