Activate yeast – Heat ¾ cup milk until warm but not hot (100 °F / 38 °C). In ½ cup of the warm milk, stir 1 teaspoon of granulated sugar and 1 ½ teaspoon active dry yeast. Let rest in a warm place for about 10 minutes, until foamy.
Make the dough – Melt ½ stick unsalted butter and let it cool slightly. It can't be too hot, just melted. Stir in the remaining milk and 2 Tablespoon spiced rum, then mix in 3 egg yolks.
In a large bowl, combine 3 cups all-purpose flour, ½ teaspoon salt, 2 teaspoons lemon zest, and the rest of 3 Tablespoons granulated sugar. Make a well in the center and pour in the activated yeast and the egg and milk mixture. Mix roughly with a fork until combined, then knead the dough for 8 to 10 minutes. You can use a stand mixer fitted with a dough hook on medium speed, or knead by hand using a wooden spoon, the old Czech way.
Let the dough rise – Transfer the dough to a clean bowl, cover with plastic wrap, and let it rise in a warm place for 1 to 2 hours, until roughly doubled in size. After about 45 minutes, briefly knead the dough to deflate it, then let it continue rising, covered.
Make cinnamon sugar – While the dough is rising, mix 1 cup granulated sugar and 1 teaspoon ground cinnamon in a bowl.
Shape the šišky – Transfer the risen dough to a lightly floured surface. Cut into pieces about 2½ ounces (70 g) each. Shape into balls, cover, and let rest for 15 minutes. Roll each ball into a strand about ½ inch thick and twist into a loose knot or simple twist.
Heat the frying oil – Heat 4 cups frying oil in a deep pan to about 350 °F (175 °C). – use a thermometer if you have one. The dough should sizzle gently when added.
Fry the šišky – Fry in batches, turning halfway so they brown evenly. Do not overcrowd the pan. Fry for 1½ to 2 minutes per side. Test the first piece by tearing it open at the thickest part. The inside should be fully cooked and soft, not doughy.
Drain and finish – Remove from the oil and place on paper towels. While still warm, sprinkle with powdered sugar or coat in cinnamon sugar.