Carefully pour in the remaining 1/4 cup water--it will steam and bubble. Carefully add the half-and-half and cook, stirring, until the syrup Re-melts. Whisk some of the hot half-and-half mixture into the egg yolks. Pour the mixture into a double boiler and cook over barely simmering water, stirring constantly, until the custard coats the spoon. Immediately place the pan in a pan of cold water and stir to cool. Stir in the cream and vanilla. Cover and refrigerate for 2 to 3 hours, or until thoroughly chilled. In a saucepan, melt the butter over medium heat and saute the nuts until golden brown; let cool. Freeze the mixture in an ice cream maker according to the manufacturer's instructions. When partially frozen, mix in the nuts.