Line a 9-inch x13-inch/ (23cm x 33cm pan) with a sheet of parchment paper long enough to hang over the sides.
Place the flour and yeast in a mixing bowl. Pour the milk in a thin stream, while stirring with a wooden spoon. Add ¼ cup plus 2 tablespoons (75grams) of the sugar and the egg yolk
to the bowl. Stir to mix until it comes together into a shaggy dough. Add the melted butter and the salt. Stir until a rough ball starts to form.
Scrape the dough onto a floured surface, and knead for a few minutes, until smooth. You may need to add a little flour to keep the dough from sticking, but don't add too much; you want the dough to be soft. Form the dough into a ball and place it in the prepared pan. Cover with a clean dishcloth and put in a warm, draft-free spot for 1 hour.
Preheat the oven to 350°F (l80°C). Remove the paper from the pan, lay it on your work surface, and roll out the dough until it fits the indentations of the pan on the paper, and then transfer the paper and dough back to the pan. The dough will be quite thin. Make dimples all over the dough using your fingertip.
Evenly dot the surface of the dough with the cold butter. Sprinkle the remaining ¼ cup (50grams) sugar over the top. Cover the pan with the dishcloth again and let sit for 20 minutes.
Bake 20 to 25 minutes, until the cake is golden brown and butter & sugar are bubbling.
Let cool on a rack for 15 minutes. Use the edges of the parchment to lift the cake out of the pan. Cut into squares and serve warm or at room temperature. Best served the day it’s made.