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Combine the warm milk, yeast, and 1 teaspoon of sugar in a small bowl and and set aside for five minutes. While yeast is proofing, whisk together the butter, egg yolks, and vanilla extract in a separate bowl. In a large bowl or bowl of a stand mixer fitted with the paddle attachment, combine 1/4 cup of sugar, flour, cinnamon, and salt.
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When the yeast mixture is foamy, add that and the butter mixture to the dry ingredients. Mix on low speed just until a soft, sticky dough forms.
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Dust countertop with flour and knead by hand (adding flour as needed) for 5 to 7 minutes until you have a smooth dough.
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Transfer dough to a greased bowl, cover with a damp towel or saran wrap, and let rise for two hours, in a warm place until doubled in size.
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While the dough rises, make the filling. In a large sauce pan, melt together the butter and cream cheese. Stir in the brown sugar and continue stirring until the mixture starts to bubble. Remove it from heat, stir in the pecans, and then set it aside to cool for an hour.
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After dough has doubled, punch it down and shape it into a rectangle. With a rolling pin, roll it out to a 9- x 13-inch rectangle. Spread the filling on evenly, leaving an inch along one of the long sides so that the filling doesn't ooze out. Starting opposite of that end, roll up the dough like a jelly roll.
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Transfer to a greased baking sheet and shape it in to an oval, joining the ends and pinching them together. Let rise for another half an hour.
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Preheat oven to 375° F. Whisk one egg together with the tablespoon of water in a small bowl and brush egg wash all over the top of the cake with a pastry brush.
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Bake the cake for 40 minutes until the cake is golden brown. Let the cake cool completely before decorating.
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To make the glaze, beat the cream cheese with the milk until smooth. Alternate adding powdered sugar and milk until glaze is thick but still pourable. Place the cake on a wire rack over parchment and pour glaze over cake. Decorate with sanding sugar, alternating purple, green, and gold. Working from the bottom of the cake, press the baby fully into the cake.