Step 1Mix rum extract into hot Custard Ice Cream Base in bowl. Place in freezer to chill, stirring occasionally, about 1 hour.
Step 2When ice cream mixture is cool, place in ice cream maker and freeze according to manufacturer's instructions. Immediately line 2-quart mold or bowl with 3/4 to 1 inch of ice cream, using spatula or spoon dipped in warm water if necessary, and place mold in freezer 2 to 24 hours.
Step 1Combine water and sugar in small, heavy saucepan and boil over medium-high heat until clear, 5 minutes. Remove from heat and let cool.
Step 2Stir egg yolks and espresso into syrup. Return to medium heat and whisk until thickened, 2 to 3 minutes, then remove from heat and beat until cool.
Step 3Whip cream until it forms stiff peaks, then fold into egg yolks-espresso mixture. Fill interior of ice cream mold with mixture, cover with plastic wrap and set in freezer until solid, 2 to 3 hours.
Step 1Remove plastic wrap and dip mold in hot water until bombe is loosened. Place serving plate upside down on top of mold; holding mold and plate together, invert so that bombe drops onto plate. Smooth surface with spatula and cover with chocolate sprinkles. Return to freezer for 1/2 hour or more to firm up.