To prepare the dough, bring 1 cup whole milk just to a boil over medium heat in a small pot. Watch closely to ensure that the milk doesn't boil over! Remove from heat and immediately add 6 tablespoons unsalted butter to the pot to melt. Once the butter has melted, transfer to the bowl of a freestanding electric mixer and let cool to 105 (F) to 110 (F) — you want the mixture to the point where it's warm to the touch, but not uncomfortably hot. With the mixer fitted with the paddle attachment, add 1/2 cup granulated sugar, 2 1/2 teaspoons active dry yeast, and 1 large, lightly beaten egg and mix on the mixer's lowest speed briefly until just combined. Add 3 cups all-purpose flour, 1 teaspoon crushed cardamom seeds, and 1 teaspoon kosher salt and mix on the mixer's lowest setting until just combined.
When the ingredients have been mixed enough to form a sticky dough, switch the paddle attachment out with the dough hook attachment and knead the dough on low speed for around 6 to 8 minutes, or until smooth and elastic. If the dough looks too sticky, feel free to add up to 2 tablespoons of all-purpose flour — but resist to add any more than that; it's normal for the dough to be a little sticky.
Use your hands to form the dough into a ball and transfer to a large, lightly greased bowl. Cover with plastic wrap and leave in a warm, draft-free spot until the dough has doubled in size — this could take 30 minutes or up to 2 hours, depending on the temperature. It's best to keep an eye on the dough rather than the clock.
When the dough has doubled in size, line two baking sheets with parchment paper and set aside.
Turn the dough out onto a very lightly floured surface and knead it a few times. Use a bench scraper or a serrated knife to divide the dough into 12 equal pieces, using your hands to roll each piece into a rough ball. Flatten each ball slightly and fold in thirds, like a letter. Then turn each piece over and reshape it into a ball, rolling each piece by forming a claw with your hand around the dough and moving it in a circle. Be sure to make the balls as neatly and tightly as you can — the nicer your balls, the nicer your buns will be. Divide the balls between the prepared baking sheets and cover loosely with plastic wrap. Place the sheets in a warm spot until the balls have doubled in size, about 1 hour. As the dough is rising for the second time, center two racks in the oven at the bottom third and upper third location of the oven and preheat to 375 (F).
In a small bowl, whisk together 1 large egg yolk and 2 teaspoons water. Use a pastry brush to lightly brush the tops and sides of each dough ball with the egg mixture. Place one baking sheet in the upper-third rack, and the second sheet in the lower-third rack. Bake in the preheated oven until golden brown, 18 to 20 minutes, swapping the two trays' location about halfway through the baking time. After baking, transfer each baking sheet to wire racks to cool until just warm. Use a serrated knife to cut off the third top of each bun, and pull out some of the center of each bun to make room for the filling. The semlor are now ready to be filled!