In a large mixing bowl, combine all-purpose and white whole wheat flours with salt. Cut in cold unsalted butter until the mixture resembles coarse crumbs, about 3 minutes.

In a separate bowl, whisk together the egg and cold water, then gradually add to the flour mixture until a dough forms. Wrap the dough in plastic wrap and refrigerate for at least 30 minutes.

While the dough chills, slice onions thinly and heat a skillet over medium-low heat with unsalted butter. Add the onions and stir occasionally, allowing them to cook slowly for about 45 minutes.

In the same skillet, melt additional unsalted butter over medium heat until golden brown. Stir in minced fresh sage for the final 30 seconds.

In a mixing bowl, combine the pumpkin purée, browned butter (with sage), egg, and kosher salt. Mix until smooth.

Preheat your oven to 425°F (220°C). Roll out the chilled dough into a rustic circle about 12 inches in diameter.

Spread the pumpkin filling evenly across the center, leaving a 2-inch border for the crust. Top with caramelized onions, crumbled goat cheese, a drizzle of honey, and whole sage leaves, then fold the edges of the dough gently over the filling.

Brush the exposed crust with beaten egg for a golden finish, and sprinkle flaky sea salt over the top. Transfer to a parchment-lined baking sheet and bake in the preheated oven for 25-30 minutes.

Allow to cool for 20 minutes before slicing and serve warm.