In a small bowl, mix milk with 2 tablespoons warm water. Add yeast and whisk gently until it dissolves. Mixture should foam slightly.
Using an electric mixer with paddle attachment, cream butter, sugar and salt. Scrape down sides of bowl and beat in the egg. Alternately add flour and the milk mixture, scraping down sides of bowl between each addition. Beat dough on medium speed until it forms a smooth mass and pulls away from sides of bowl, 7 to 10 minutes.
Press dough into an ungreased 9-by 13-inch baking dish at least 2 inches deep. Cover dish with plastic wrap or clean tea towel, put in a warm place, and allow to rise until doubled, 2 1/2 to 3 hours.
Heat oven to 350 degrees. To prepare topping, in a small bowl, mix corn syrup with 2 tablespoons water and the vanilla. Using an electric mixer with paddle attachment, cream butter, sugar and salt until light and fluffy, 5 to 7 minutes. Scrape down sides of bowl and beat in the egg. Alternately add flour and corn syrup mixture, scraping down sides of bowl between each addition.
Spoon topping in large dollops over risen cake and use a spatula to gently spread it in an even layer. Bake for 40 to 45 minutes; cake will rise and fall in waves and have a golden brown top, but will still be liquid in center when done. Allow to cool in pan before sprinkling with confectioners’ sugar for serving.