Boston Cream Pie

INGREDIENTS

• :
• 2 cups half-and-half
• ½ cup granulated sugar
• Pinch of salt
• 5 egg yolks
• 3 tablespoons cornstarch
• 4 tablespoons cold unsalted butter, cut into 4 pieces
• 1½ teaspoons vanilla extract
• ½ cup plain cake flour
• ¼ cup all-purpose flour
• 1 teaspoon baking powder
• ¼ teaspoon salt
• 3 tablespoons whole milk
• 2 tablespoons unsalted butter
• ½ teaspoon vanilla extract
• 5 eggs, at room temperature
• ¾ cup granulated sugar
• 1 cup heavy cream
• ¼ cup light corn syrup
• 8 ounces semisweet chocolate, chopped into small pieces