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  1. To make the filling: Combine the prunes, brown sugar, water, and lemon juice in a medium saucepan and bring the mixture to a boil over medium heat, stirring constantly. Simmer until the mixture is thick enough to spread, about 8 minutes. Remove from the heat and set aside to cool to room temperature.

  2. To make the dough: Warm the milk for 45 seconds in the microwave and pour over the sugar, salt, and butter in a large bowl.

  3. Let cool to lukewarm, then add the egg, vanilla, and yeast. Add half the flour and mix well.

  4. Add the remaining flour, a little at a time; mix until you have a soft smooth dough, adding the last 1/4 cup of flour as you knead the dough for 8 minutes. After kneading, it will be soft, but shouldn't be sticky when lightly touched.

  5. Place the dough into an greased bowl, cover the bowl, and let rise until doubled, about 1 hour.

  6. To assemble: Deflate the dough after its rise and place on a piece of parchment. Roll it out to a 16" x 8" rectangle. Transfer the parchment with the dough on it to a baking sheet.

  7. With the short edge facing you, spread the filling lengthwise down the center third of the rectangle, leaving 1" across the top and bottom uncovered. Sprinkle with the nuts.

  8. Cut 1" crosswise strips from the edge of the filing to the outside edges, down the length of the dough, making sure you have the same number of strips down each side.

  9. Fold the top and bottom edge of the dough over the filling. Beginning on the left, lift the first dough strip and gently bring it across the filling diagonally. Repeat on the other side with the top dough strip, so that the two strips crisscross each other. Continue down the entire braid, alternating strips to form the loaf. Tuck the ends of the bottom strips under the loaf. See our video, How to make a filled braid, for a step-by-step walkthrough of this process.

  10. Cover with an inverted baking sheet or greased plastic and let rise for 40 to 45 minutes, or until puffy. Partway through the rise, preheat the oven to 350°F.

  11. For the topping: When the dough looks puffy, brush it all over with the beaten egg mixture.Mix the sugar and cinnamon together and sprinkle all over the top.

  12. Bake the braid for 24 to 26 minutes, until golden brown and the center measures 190°F on a digital thermometer. Remove from the oven and let cool on a rack.

  13. Remove from the oven, and cool on a rack.

  14. Store the coffee cake, well-wrapped, at room temperature for up to 5 days or in the freezer for up to a month.