Pastry
Heat half-and-half in medium saucepan over medium heat until just simmering. Meanwhile, whisk yolks, sugar, and salt in medium bowl until smooth. Add flour to yolk mixture and whisk until incorporated. Remove half-and-half from heat and, whisking constantly, slowly add 1/2 cup to yolk mixture to temper.
Whisking constantly, return tempered yolk mixture to half-and-half in saucepan.
Return saucepan to medium heat and cook, whisking constantly, until mixture thickens slightly, about 1 minute. Reduce heat to medium-low and continue to simmer, whisking constantly, 8 minutes.
Increase heat to medium and cook, whisking vigorously, until bubbles burst on surface, 1 to 2 minutes. Remove saucepan from heat; whisk in butter and vanilla until butter is melted and incorporated. Strain pastry cream through fine-mesh strainer set over medium bowl. Press lightly greased parchment paper directly on surface and refrigerate until set, at least 2 hours and up to 24 hours.
Assemble
Place one cake round on large plate. Whisk pastry cream briefly, then spoon onto center of cake. Using offset spatula, spread evenly to cake edge. Place second layer on pastry cream, bottom side up, making sure layers line up properly. Press lightly on top of cake to level. Refrigerate cake while preparing glaze.
Glaze
Bring cream and corn syrup to simmer in small saucepan over medium heat. Remove from heat and add chocolate. Whisk gently until smooth, 30 seconds. Let stand, whisking occasionally, until thickened slightly, about 5 minutes.
Pour glaze onto center of cake. Use offset spatula to spread glaze to edge of cake, letting excess drip decoratively down sides. Chill finished cake 3 hours before slicing. Cake may be made up to 24 hours before serving.
