In a small bowl, stir the yeast and sugar into the warm water. Let sit until foamy, about 10 minutes. While the yeast proofs, whisk together the flours, sea salt, and minced sage leaves in a large bowl or stand mixer.
Once the yeast is foamy, stir in the pumpkin puree, honey, oil, and egg plus yolk. Pour into the dry mixture, and knead for seven to ten minutes, until the dough is smooth and elastic. Shape into a ball and place in a well-oiled bowl, covered with plastic wrap. Let rise for 1 ½-2 hours, or until doubled in size.
Once risen, remove the dough from the bowl and shape into a 12"-long rectangle. Line a large baking sheet with parchment paper, and transfer the dough onto the baking sheet. Cut the dough into three even pieces, lengthwise, which will be your strands to braid. Roll each strand out until it’s about 1-2" thick.
Create a trench down the middle of each strand, and fill with evenly divided amounts of goat cheese, sage leaves, and a light sprinkling of flaky sea salt and freshly cracked black pepper. Roll strands closed, lengthwise, and then pinch them together at the top and braid as usual. Tuck ends under at the bottom, and pinch strands together. Cover the braided challah with a clean, damp dishtowel, and let rise again, another 45 minutes.
Preheat oven to 350ºIn a small bowl, mix the egg wash (1 yolk + 1 teaspoon water). Once challah is finished with its second rise, brush with the egg wash, and bake for 35 to 40 minutes, until golden brown.