Make ahead: About two hours before preparing the dish, remove the butter, eggs, and mayonnaise from the fridge to bring them to room temperature. Just before starting, heat the milk until it is lukewarm.
Making yeast dough: Begin by placing 2 ⅓ cups all-purpose flour in a mixing bowl and making a wide well in the center. Combine ⅓ cup milk (lukewarm) with half a teaspoon of sugar and pour the mixture into the well. Sprinkle 1 ½ teaspoons active dry yeast over the milk. Using a fork, gradually incorporate a small amount of flour into the milky mixture until a semi-liquid dough forms in the center.
Cover the bowl with plastic wrap and let it rise in a warm place for about 30 minutes, until the yeast becomes bubbly.
Add 3 Tablespoons granulated sugar, ¼ teaspoon salt, ⅔ cup mayonnaise, and 1 egg to the bowl.
Knead on medium speed for 10 minutes in a stand mixer with the dough hook attached. After this time, the dough will be smooth, elastic, and slightly sticky.
Dump the dough onto a floured work surface and shape into a ball. Pull the edges out from the sides and bring them together over the center of the dough. Then gently turn the dough ball over, seam side down.
Cover with a tea towel and let rise in a warm, draft-free place for 45 minutes.
Line a baking sheet with parchment paper. Transfer the proofed dough to the center and flatten slightly to a height of about 1 ½ inches (4 cm). Cover and let it rise for another 30 minutes.
Making pudding buttercream: While the dough is rising, let's make the buttercream. Pour 1 ½ cups milk for the cream into a saucepan and heat over medium heat. Once the milk is lukewarm to warm, pour half of it into a clean bowl and whisk in 6 ½ Tablespoons cornstarch, ½ cup granulated sugar and ½ teaspoon vanilla extract.
Once the remaining milk on the stove reaches a boil, take the saucepan off the heat and blend in the sweet milk mixture with the cornstarch. Place it back on the stove, lower the heat to simmer, and cook for approximately 2 minutes, stirring constantly.
Allow the cream base to cool to room temperature. Stir occasionally to encourage cooling and prevent skin from forming on the surface. Alternatively, cover the surface tightly with plastic wrap to prevent a skin from forming.
Whip ¼ cup whipping cream. This works best in a narrower, taller container with an electric mixer equipped with whisk attachments.
Using the same whisk, gradually incorporate ¾ stick unsalted butter (softened) into the cooled cornstarch pudding base. Finally, fold in the whipped cream by hand. Place the pudding buttercream in the refrigerator.
Making cinnamon crumble: To make the crumbles, combine 2 Tablespoons granulated sugar, 2 Tablespoons unsalted butter, 3 Tablespoons all-purpose flour, and ¼ teaspoon ground cinnamon in a bowl. Work with your fingers until the ingredients form clumps.
Finishing the Prague kolach: Brush the proofed kolach on all sides with a bit of beaten egg and generously sprinkle with cinnamon crumbs. Bake in a
360 °F preheated oven for 25 minutes. Let the kolach cool on a cooling rack. Using a large serrated knife, slice the cooled cake and spread the buttercream evenly to the edges with a pastry spatula. Cover and chill for approximately an hour.