2(small-to-medium) crunchy, tart apples (such as Granny Smiths)peeled & diced (for about 2 cups total)
FOR THE GLAZE:
1/2cup(1 stick) butter
1cuppacked brown sugar
2 1/2cupspowdered sugarsifted
1teaspoonpure vanilla extract
Flaked sea saltoptional garnish
Adjust the rack to the center position of the oven and preheat the oven to 375°F. Grease a rimmed 18x13x1-inch half sheet pan with softened butter.
In a large pot set set over medium heat, melt the butter. Add the water, increase the heat, and bring to a boil. Remove pot from the heat and briskly stir in the flour until smooth, followed by the sugar, cinnamon, and sour cream. Stir in the eggs until fully incorporated (temper them first if the batter is still hot). Mix in the vanilla. Then sprinkle the baking soda and salt over the top of the batter (make sure there are no lumps!) and stir them in until all ingredients are well blended. Fold in the diced apples.
Pour the batter into the prepared sheet pan and smooth the top. Bake for 18 to 22 minutes or until a toothpick inserted into the center of the cake comes out clean. Set cake pan on a wire rack to cool.
While the cake cools, make the glaze. Place a medium pot over medium heat and add the butter, brown sugar, and salt. Stir over medium heat until smooth and melted, then bring to a boil, stirring frequently. Remove the pot from the heat and carefully stir in the half-and half. Return the pot to the heat and bring to another boil, stirring frequently. Remove the pot from the heat once more and stir in the sifted powdered sugar and the vanilla until smooth. Immediately pour the glaze over the cooling cake and spread into a thin, even layer.
Allow the glaze to set (at room temperature or uncovered in the refrigerator) before slicing. Sprinkle individual slices with flakes of salt before serving, if desired. Cover tightly and refrigerate any leftovers.