Step 1

Brush a 13-by-9-inch glass baking dish with butter. Line with parchment paper, leaving a 2-inch overhang on each of the long sides, and butter. Set aside.

Step 2

Make the cake: In a small bowl, stir together milk and yeast; let stand until slightly foamy, about 5 minutes.

Step 3

In the bowl of an electric mixer fitted with the paddle attachment, beat butter, sugar, and salt until light and fluffy, about 2 minutes. Add eggs, one at a time, beating well after each addition. Add flour in two additions, alternating with the milk mixture. Beat on medium speed until it forms a soft dough, 3 to 5 minutes.

Step 4

Press dough into prepared baking dish and cover loosely with plastic wrap. Set aside in a warm place until puffy and full of air, about 1 hour.

Step 5

Make the topping: Preheat oven to 350 degrees. In the bowl of an electric mixer fitted with the paddle attachment, cream the butter, sugar, and salt on medium-high speed until light and fluffy, about 2 minutes. Add egg, egg yolk, and vanilla and beat to combine, scraping down sides of bowl. Add flour in two additions, alternating with corn syrup. Beat until thoroughly combined.

Step 6

Spread topping evenly over risen dough using an offset spatula. Bake until just golden around the edges, about 20 minutes. Let cool completely in baking dish on a wire rack before dusting with confectioners' sugar and serving.