To make the dough:

• Add half of the warm milk into a small bowl along with the dry yeast and ½ teaspoon of sugar. Stir well to dissolve the yeast and set aside until the mixture gets foamy (approximately 5-7 minutes).
• In another small bowl, whisk the melted butter (cooled slightly), almond extract, remaining milk, and eggs until combined. Set aside.
• In a large mixing bowl (or the bowl of a stand mixer) sift the flour, 3 tablespoons of sugar, ½ teaspoon salt. Add the milk and yeast mixture along with the egg and butter mixture to the bowl with the flour and stir well until it comes together into a shaggy dough.
• Add the bowl to the stand mixer and using the dough hook attachment knead the dough (on medium speed) until it transforms into a smooth and elastic dough. This will take approximately 7 - 10 minutes of kneading.
• Turn the smooth dough out onto the counter and grease the inside of the bowl with softened butter. Return the dough to the buttered bowl and cover with plastic wrap. Allow the dough to rest for 30 minutes.
• Meanwhile, whisk 10 tablespoons of softened butter along with ¼ teaspoon of kosher salt until it's light and fluffy. Use some additional softened butter to also liberally butter the bottom and sides of the jelly roll pan.
• After 30 minutes, gently turn the dough out onto the prepared buttered pan and press the dough evenly into the entire surface of the pan and slightly up the sides. Use your fingertips to gently press dimples evenly across the surface of the dough. Cover with plastic wrap and allow the dough to rest again for 20-30 minutes.
• While the dough is resting, preheat the oven to 350 degrees Fahrenheit (175 degrees Celsius).
• After resting, uncover the dough and use an offset spatula to evenly spread the whisked and softened butter over the entire surface of the dough. Next sprinkle the 1 cup of granulated sugar along with the sliced almonds evenly over the buttered surface of the dough.
• Bake in the preheated oven for 25 minutes, or until the kuchen is golden brown and the sugar is almost fully melted. Cool on a wire rack for at least 30 minutes before slicing. Zuckerkuchen is best served slightly warm.