Step 1

Remove the cake from the oven when the perimeter is golden brown and the center is still slightly loose; the topping will continue to set as the cake cools.

Step 2

For the dough: Adjust oven rack to lower-middle position and heat oven to 200 degrees. When oven reaches 200 degrees, shut oven off. Line 8-inch square baking pan with foil sling. Grease foil and medium bowl.

Step 3

In bowl of stand mixer fitted with paddle attachment, mix milk and yeast on low speed until yeast dissolves. Add sugar, eggs, vanilla, salt, and flour and mix until combined, about 30 seconds. Increase speed to medium-low and add butter, 1 piece at a time, until incorporated, then continue mixing for 5 minutes. Transfer batter to prepared bowl, cover with plastic, and place in warm oven. Let rise until doubled in size, about 30 minutes. Spread batter in prepared pan. Heat oven to 350 degrees.

Step 4

For the topping: In bowl of stand mixer fitted with paddle attachment, beat granulated sugar, butter, and cream cheese on medium speed until light and fluffy, about 2 minutes. Reduce speed to low and add corn syrup, egg, and vanilla until combined. Add flour and pudding mix and mix until just incorporated. Portion dollops of topping evenly over batter, then spread into even layer.

Step 5

Once oven is fully heated, bake until exterior is golden and center of topping is just beginning to color (center should jiggle slightly when pan is shaken), about 25 minutes. Cool in pan at least 3 hours. Use foil overhang to lift cake from pan. Dust cake with confectioners’ sugar. Serve. (Cake can be refrigerated for 2 days.)