Make dough: combine sour cream, butter, salt, and 3 tbsp erythritol in a saucepan over medium-low until butter melts, 5 minutes. Cool 15 minutes. Dissolve yeast and remaining 1/2 tbsp erythritol in warm water and proof 5 minutes until foamy. Combine sour cream mixture, yeast mixture, egg, and 1/3 of the bread mix in a stand mixer with paddle. Beat until smooth. Gradually add remaining mix. Turn out and knead 10 minutes until smooth and elastic. Cover and rise until doubled, about 1 hour.

Make filling: beat cream cheese, erythritols, cinnamon, and vanilla until smooth. Beat in egg.

Punch dough down. Roll into a large rectangle. Spread filling evenly leaving a 1-inch border. Sprinkle with pecans. Roll up jelly-roll style from one long side. Form into a ring on a parchment-lined baking sheet, moistening and pinching ends together. Cover and rise until doubled, 1 hour.

Preheat oven to 350°F. Bake 25 minutes until deep golden brown. Cool completely on wire rack, about 1.5 hours.

Make glaze: whisk confectioners erythritol, melted butter, and vanilla. Add cream 1 tsp at a time until pourable but still opaque. Pour over cooled cake. Sprinkle with alternating bands of purple, green, and gold sparkling erythritol.