Yeast starter: Heat ⅓ cup milk in a small saucepan until it is lukewarm (110-115°F/43°C). Stir in ¼ teaspoon powdered sugar and 1 ½ teaspoons active dry yeast, then let it sit in a warm spot for about 10-15 minutes, until foam and bubbles form on the surface.
Yeast dough: Sift 2 ½ cups all-purpose flour and ⅓ cup powdered sugar into a mixing bowl. Add ¼ teaspoon salt, ¼ teaspoon vanilla extract, and grated 1 Tablespoon lemon zest. In a saucepan, melt ¾ stick unsalted butter completely, then stir in ¼ cup milk and whisk in 2 yolks and 2 Tablespoons rum. Pour this mixture into the bowl with the flour, and finally, add the activated yeast. Use a wooden spoon or a kitchen stand mixer with a hook attachement to knead the dough until smooth and elastic. If the dough sticks while kneading, sprinkle a little flour and keep working it.
Lightly flour the dough, cover with a clean cloth, and let it rise in a warm spot until it doubles in size, about 1 ½ hours.
Cheese filling: Place 27 ounces farmers cheese, ¾ cup powdered sugar, 1 Tablespoon cornstarch, 1 yolk, 1 Tablespoon lemon zest, ¼ teaspoon vanilla extract, and 1 cup half-and-half in a bowl and stir until well combined. Gradually add enough half-and-half or milk to create a creamy, spreadable mixture. Let the cheese filling sit on the kitchen counter until it reaches room temperature before applying it to the kolach.
Shape the kolach: Turn the dough onto a lightly floured surface and divide it into three parts. Prepare a 12-inch (30 cm) round baking sheet and lightly brush it with a little unsalted butter or solid fat. Place one piece of dough in the center and roll it out thinly. Use your fingers or the edge of your palm to create small, raised edges around the kolach.
Brush the edges of the cakes with 1 egg white for a glossy finish after baking.
Spread ⅓ of the cheese filling all over the kolach. A flat offset spatula works best for this.
Put 1 ½ cup plum butter in a piping bag with a plain tip and pipe patterns over the cheese filling. Sprinkle each kolach with ⅓ of 3 Tablespoons raisins and 2 Tablespoons sliced almonds.
Preheat the oven to
360 °F with both upper and lower heat. Transfer the decorated kolach, along with the baking paper, to a baking tray. Bake for 18 minutes, then remove from the oven, leaving the kolach on the baking sheet. Sour cream topping: In a bowl, mix 1 cup sour cream with a shot of 1 Tablespoon rum. Spoon a third of the mixture over the hot kolach, spreading it carefully to avoid disturbing the pattern. As a final touch, give the kolache a nice dusting of ⅓ cup powdered sugar.
Bake the remaining kolache the same way.