If you are using fresh yeast, crumble it into the warm milk in a stand mixer bowl and stir until dissolved. If you are using active dry yeast, whisk it into the milk in a bowl, cover it, and let it sit in a warm spot for about 15 minutes until frothy. After that, move it to the mixer.

Add the sugar, cardamom, soft butter, and egg yolk to the milk mixture, and mix until combined. Then stir the salt into the flour and add the flour gradually. Knead on low speed for 5 to 6 minutes until the dough is smooth but still a little sticky. If it feels too loose to handle, add just a little more flour.

Cover the bowl and let the dough rise in a warm place for about 30 minutes, or until doubled. Meanwhile, make the topping so it is ready when the dough is done rising.

Beat the softened butter with the scant 1 cup brown sugar, syrup, cinnamon, and vanilla until very soft and spreadable. Set it aside. Then knead the dough briefly on a floured surface, roll or stretch it to fit the pan, and ease it into the corners. Press shallow dimples all over the surface with your fingertips, just like focaccia.

Spread the topping over the dough, but keep a little aside in case you need it later. If the topping is too stiff, warm it briefly in the microwave. Scatter the remaining 2 tablespoons sugar on top, cover, and let it rise for another 20 minutes. Heat the oven to 400°F, then bake for 20 to 25 minutes until the cake is cooked through and the top is sticky and glossy.

If the topping looks dry during baking, dot the top with the reserved topping. If it browns too fast, lower the oven temperature or tent it with foil. When the cake is done, cool it in the pan for 10 to 15 minutes, then cut it into squares and serve warm.