Mährisk sockerkaka

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1. 1
   Whisk together ½ cup plus 1 Tbsp. (113 g) granulated sugar with ⅓ cup warm water in the bowl of a stand mixer until mostly dissolved. Sprinkle 1¾ tsp. active dry yeast over and let sit 5 minutes.
2. 2
   Meanwhile, combine ¾ cup whole milk and 3 Tbsp. unsalted butter, cut into small pieces, in a medium microwave-safe bowl. Microwave on high power in 30-second bursts until butter is melted and milk is warm, about 1 minute. (Milk should be warm, not hot. If the milk is too hot, let it cool until it’s the temperature of a warm bath.)
3. 3
   Add milk mixture, 1 large egg, 2⅓ cups plus 3 Tbsp. (315 g) all-purpose flour, ⅓ cup instant potato flakes, 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt to yeast mixture. Fit bowl onto stand mixer and attach dough hook. Starting on low speed and gradually increasing to high speed as flour is incorporated, beat until dough is somewhat smooth but still very sticky (somewhere between the texture of bread dough and cake batter), about 4 minutes. Stop motor, scrape down sides of bowl, and mix on low speed until dough is completely smooth but still sticky, 3–4 minutes more. (Dough will still stick to the sides of the mixer when it’s done.) Spray a large bowl with nonstick vegetable oil spray and scrape dough into bowl. Tightly cover with plastic wrap and let rise in a draft-free spot until puffy but not quite doubled in volume, 30–45 minutes.
4. 4
   Coat an 8x8" baking pan with nonstick spray. Scrape dough into pan, pressing it evenly across bottom with wet fingers. Cover with plastic wrap and let rise until puffy but not quite doubled in volume, 30–45 minutes.
5. 5
   While the dough is rising, whisk ½ cup plus 2 Tbsp. (packed; 125 g) light brown sugar, 1½ tsp. ground cinnamon, and ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt in a medium bowl.
6. 6
   Place a rack in bottom third of oven; preheat to 375°. Uncover dough and sprinkle brown sugar mixture evenly over surface. Drizzle 4 Tbsp. unsalted butter, melted, slightly cooled, evenly over. Using your fingers, dimple surface of dough, pressing all the way to the bottom of pan to create deep divots, (like focaccia).
7. 7
   Bake cake until puffed and dark golden brown, 32–37 minutes. Transfer pan to a wire rack and let cake cool in pan until no longer too hot to the touch. Turn cake out onto rack and let cool completely. Cut into 9 squares (3x3 grid) to serve. Do Ahead: Cake can be baked 2 days ahead. Stored tightly wrapped at room temperature.