Step 1

Preheat oven to 350°. Line bottom and sides of an 8x8" baking dish with parchment paper. Whisk 1 cup (125 g) all-purpose flour, 1 tsp. baking powder, 1 tsp. baking soda, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and ½ tsp. ground cinnamon (if using) in a medium bowl.

Step 2

Melt ⅓ cup (5 Tbsp. plus 1 tsp.) unsalted butter in a small skillet over low heat, then pour into a large bowl; reserve skillet. Add ½ cup (100 g) light brown sugar, ½ cup (100 g) granulated sugar, and 1 tsp. vanilla extract to large bowl and whisk to combine. Whisk in 2 large eggs. Add dry ingredients and whisk until mostly combined. Add 3 large apples, preferably Granny Smith, peeled, grated on the large holes of a box grater, and whisk until apples are distributed and no spots of dry flour remain. Scrape batter into prepared baking dish; smooth top.

Step 3

Bake cake until a tester inserted into the center comes out clean, 30–35 minutes. Transfer to a wire rack and let cake cool in pan. Invert cake onto a plater and remove parchment paper. (Turning the cake bottom side up ensures a nice flat surface for glazing.)

Step 4

Just before serving, melt remaining 2 Tbsp. plus 2 tsp. unsalted butter in reserved skillet over medium heat; cook, stirring constantly, until milk solids are deep brown, about 3 minutes. Add ¼ cup heavy cream, a pinch of kosher salt, and remaining ½ cup (100 g) light brown sugar. Stirring constantly, bring mixture to a boil and cook until slightly thickened and sugar is melted, 1–2 minutes (an instant-read thermometer should register 225°). Pour glaze over cake and spread to edges with an offset spatula. Sprinkle flaky sea salt over.

Step 5

Let glaze cool at least 5 minutes before cutting cake into squares.