Make the dough: Place sour cream, warm water, softened butter, egg, flour, sugar, salt, and yeast into a bread machine in the order listed, or follow the order recommended by the manufacturer if different. Run Dough cycle. Remove dough from the machine after the cycle is done, about 90 minutes.

Transfer dough to a lightly floured surface; roll out to a 10x28-inch rectangle.

Make the filling: Mix sugar, melted butter, and cinnamon together in a bowl. Spread mixture over dough, then sprinkle pecans over top. Starting at a long edge, roll dough over filling into a log. Transfer to a greased baking sheet with the seam facing down.

Moisten dough at each end of the log; pull ends together to form a ring and pinch to seal. Cover with a cloth and let rise in a warm place until doubled in volume, about 30 minutes.

Preheat the oven to 375 degrees F (190 degrees C).

Bake cake in the preheated oven until golden brown on top, about 15 minutes. Remove from the oven and let cool on a wire rack for 10 minutes.

While the cake is cooling, make the glaze: Combine confectioners’ sugar, melted butter, and vanilla in a bowl. Stir in just enough milk to make a smooth but not watery glaze.

Spoon glaze onto warm cake, allowing it to dribble down the sides. Immediately sprinkle alternating bands of purple, green, and yellow colored sugar over glaze. Allow cake to cool completely before serving.