Add 3 ½ cups all-purpose flour to a bowl and make a small well in the center. Warm 1 cup milk to 100-110°F (38°C). Pour ¼ cup into the well, add a pinch of sugar and 1 ½ teaspoons active dry yeast, then, using a fork, stir in some flour from the edges of the well to form a semi-liquid mixture. Let it rest in a warm place until bubbly, about 15 minutes.
Heat the remaining milk briefly to make it warm. Add ¾ stick unsalted butter, cut into pieces, and let it melt—it does not need to be fully melted. Add ⅓ cup granulated sugar, ¼ teaspoon salt, ½ teaspoon vanilla extract, and 2 pieces yolk, then whisk everything together with a fork.
Pour the liquid mixture into the bowl with the activated yeast. Using a mixer with a hook attachment, knead on low until combined, then on medium-high for 8 minutes. The dough should be smooth and elastic.
Turn the dough out onto a work surface; it should not stick when kneaded well. Shape it into a ball and place it in a clean bowl. Cover with a tea towel or plastic wrap and let it rise in a warm place until doubled in size.
While the dough rises, prepare the vanilla pudding. Heat 1 ¾ cups milk in a saucepan over medium-high heat. Remove ½ cup of the warm milk and whisk it with 4 Tablespoons cornstarch, 4 Tablespoons granulated sugar, and ¼ teaspoon vanilla extract until smooth and lump-free. When the remaining milk starts to boil, take it off the heat. Gradually whisk in the cornstarch mixture, then return the saucepan to the stove and cook at a gentle boil for 1 minute, whisking constantly. Set aside. Cover the pudding surface with plastic wrap to prevent a skin from forming, and let it cool to room temperature.
Roll the dough into a neat rectangle about ¼ inch (0.5 cm) thick. Briefly whisk the pudding with a hand mixer, then spread it evenly over the dough, leaving a ½-inch (1.5 cm) free space around the edges. Sprinkle ⅓ cup golden raisins over the pudding. Starting from the longer side, roll the dough tightly, ending with the seam side down.
Use a thin, serrated knife to cut the roll into 1-inch (2.5 cm) slices. Arrange the slices on a parchment-lined cookie sheet, leaving at least 1 inch (2.5 cm) of space between them for proofing and to prevent them from sticking to each other during baking. Cover with a clean tea towel and let proof for 30 minutes.
In a small bowl, lightly whisk 1 egg white leftover from making the dough. For a glossier surface, you can use a whole egg instead. Brush the Šneky rolls on all sides. Bake in a preheated oven at
360 °F for 22 minutes. Once baked, let the rolls cool on the baking sheet or transfer them to a cooling rack.