Whisk egg yolk and 1tablespoon whipping cream in anothersmall bowl to blend. Using electric mixer,beat butter and sugar in medium bowl untilblended. Beat in yolk mixture (mixture maylook curdled). Beat in flour mixture justuntil blended (dough will be slightly sticky).Using floured hands, gather dough togetherand form into disk. Wrap in plastic; chill atleast 1 hour. DO AHEAD: Can be made 1 dayahead. Keep chilled.
Let soften slightly atroom temperature before rolling out.
Position rack in center of oven andpreheat to 375°F.
Roll out dough on lightlyfloured parchment paper to 9-inch round.Using 8 1/2-inch-diameter plate as guide, cutout round.
Transfer dough round, still onparchment, to baking sheet. Pierce doughall over with fork.
Bake until crust is goldenbrown and baked through, 28 to 30 minutes.Cool crust completely on baking sheet. DO AHEAD: Can be made 1 day ahead. Coverand store at room temperature.
Combine 1 cup sugar, 1/3 cupwater, and corn syrup in heavy mediumsaucepan. Stir over medium-low heatuntil sugar dissolves. Increase heat andboil without stirring until mixture turnsdeep amber, occasionally swirling panand brushing down sides with wet pastrybrush, about 10 minutes. Immediately pourcaramel into 9-inch-diameter cake panwith 2-inch-high sides. Using oven mitts toprotect hands, tilt pan to swirl caramel overbottom and halfway up sides of pan. Coolwhile preparing custard.
Position rack in center of oven andpreheat to 325°F.
Whisk egg yolks, eggs,1 cup cream, and 1/4 cup sugar in large bowlto blend.
Combine 1 cup cream, milk, rum,nutmeg, and 1/2 cup sugar in large saucepan.Stir rum mixture over medium heat untilsugar dissolves; increase heat and bring tosimmer. Gradually whisk hot rum mixtureinto yolk mixture.
Pour mixture through finestrainer into cake pan with caramel.
Placecake pan in large roasting pan.
Add enoughhot water to roasting pan to come halfwayup sides of cake pan. Cover roasting panloosely with foil.
Bake flan until set, about 1 hour 40minutes (center may move slightly whenpan is gently shaken, but top will feel setwhen lightly pressed).
Remove from oven;let flan stand in roasting pan with water10 minutes.
Remove cake pan from roastingpan.
Transfer directly to refrigerator; chilluncovered overnight. DO AHEAD: Can bemade 2 days ahead. Cover and keep chilled.
Combine all ingredients except nutmeg in large bowl.Using electric mixer, beat until peaks form.DO AHEAD: Can be made 2 hours ahead.Cover and chill. Rewhisk to thicken, ifnecessary, before using.
Run small knife around flan to loosenfrom pan.
Place baked crust atop flan inpan.
Place large platter atop flan with crust.Using both hands and holding platter andpan with flan firmly together, invert flanwith crust onto platter. Scrape any caramelremaining in pan over flan. Top center offlan with mound of rum whipped cream.