DAY 1: Stir together all ingredients for pâte fermentée and mix on low speed for 1 minute, adjusting flour or water, as needed.
Knead on medium speed for 4 minutes, dough should be soft and pliable.
Transfer dough to lightly oiled bowl, cover and ferment at room temperature for 1 hour.
Knead lightly to degas, cover and refrigerate overnight (or up to 3 days).
DAY 2: Remove pâte fermentée from refrigerator 2 hours before using.
In a small bowl, mix potato flakes with water. Set aside.
Combine all dough ingredients (except potatoes) in mixer bowl. Knead on low speed for 3 minutes, add potatoes and knead for another 3-4 minutes.
Place dough in lightly oiled bowl, cover, and let rise for about 1 ½ hour.
Transfer dough to a floured work surface and divide into 4 pieces.
Cover pre-shaped dough pieces and let them rest for 20 minutes.
Fold each dough round from 3 sides to the middle to make a triangle.
Place on parchment lined baking sheet, seam side down. Spread beer paste over loaves and dust with rye flour.
Proof breads at room temperature for about 1 ¼ hours.
Preheat oven to 445ºF/230ºC.
Bake for 10 minutes, then rotate breads and continue baking for about 15 minutes more.
Let cool on wire rack for at least 1 hour before cutting.
