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Transfer the warm potato puree to a stand mixer and beat in the butter. With the mixer running, add 1 egg at a time, incorporating each fully before adding the next. Beat in 1 cup of the flour and let stand for 10 minutes. In a separate bowl, stir the yeast and sugar into 1/2 cup warm water and let stand for 5 minutes. Stir in 1 cup of the flour into the yeast, then add to the potato puree. Add the remaining 2 cups flour to the mixer. Switch to a dough hook and beat until smooth, about 10 minutes.
Transfer the dough to a lightly greased bowl, cover and set aside in a warm spot (75 to 80 degrees F) until doubled in size, about 1 hour.
Roll the dough into a 24-by-16-inch rectangle on a lightly floured surface.
For the pretzel sablee: Combine the brown sugar, butter and cinnamon in a bowl and beat until smooth. Add the pretzel meal and mix until just combined.
Spread the pretzel sablee in as even a layer as possible on the rolled-out dough. Roll the dough into a 24-inch log. Cut the log into 12 pieces and lay, evenly spaced, cut side up, on a lightly greased baking sheet. Leave to rise a second time, until the pieces are nearly touching, about 45 minutes.
Preheat the oven to 375 degrees F.
Bake the cinnamon rolls until golden brown, rotating once. Check on the rolls after 20 minutes. Depending on your oven, they may require an additional 10 to 15 minutes.
Meanwhile, for the glaze: combine the apricot preserves with 2 tablespoons water in a small saucepan over medium-low heat. Warm, stirring, until the mixture turns liquid. Press through a mesh strainer.
Once the cinnamon rolls are out of the oven, brush them with the warm glaze and dust with coarse sugar to mimic pretzels. Leave to rest for 20 minutes to allow the glaze time to set.