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Remove the dough from the bowl and place it on a clean lightly floured work surface. Pat it into a rectangle shape, then roll it out into a long skinny roughly 22-inch by 9-inch rectangle.
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Using a rubber spatula, evenly spread the pumpkin mixture over the rectangle, leaving an empty 1-inch border around the edge. Evenly sprinkle the crumbled feta and grated gouda cheese over the pumpkin.
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Roll up the dough along the longest edge to form a long log, and pinch each end of the log to seal in the filling. Place the log on a lightly greased piece of parchment paper on a large baking sheet. Using kitchen shears, starting from 1” away from the end, cut through the top layer of the log and end about 1” away from the opposite end of the log, exposing the layer of pumpkin filling inside.
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While keeping the cut side facing up, move the ends to form an “S” shape. Then, tuck the ends of the log under the middle part of the “S” to form an “8” shape. Cover with lightly greased plastic wrap or tin foil and allow to rise at room temperature out of direct sunlight until almost doubled in width, about 1 hour.
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Preheat the oven to 350 degrees Fahrenheit. Uncover the bread and bake for 25 minutes. Then remove it and place tin foil over the top to prevent over-browning of the filling, and bake until the internal temperature of the middle of the loaf reaches 195 degrees Fahrenheit, about 20 to 25 minutes more.
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Remove it from the oven and allow the bread to cool to warm before slicing and serving. Will keep in an airtight container in the refrigerator for up to 1 week.