In the bowl of a stand mixer, whisk together the flour, sugar, yeast and salt until well combined.
500 g flour, 100 g brown sugar, 18 g yeast, 5 g salt
Add the pumpkin, milk and eggs. Using the dough hook attachment, mix/knead on low until it comes together as a cohesive dough. There should not be any dry ingredients visible and, while the dough may be a bit loose and sticky, it will ball up on and climb the dough hook.
200 g pumpkin puree, 110 g whole milk, 2 eggs
Add the butter, one tablespoon at a time, mixing/kneading on low after each addition util the butter disappears fully into the dough.
120 g butter
After all the butter is incorporated, knead until the dough is silky smooth, stretchy and pulling away from the sides of the bowl (15-20 minutes)
Shape the dough into a ball, place in a large greased bowl and cover with plastic wrap. Allow it to rest on the counter for about 20 - 30 minutes, then transfer the bowl to the refrigerator to continue rising overnight.
Remove the dough from the refrigerator and shape into 2 equal sized loaves (I like to braid the dough and tuck the ends under) and put the shaped loaves into two 9"x5" loaf pans).
Cover the loaves loosely with plastic wrap and allow to rise until nearly doubled in size. The dough should be very puffy and soft with an almost marshmallow like texture. (The time this takes can vary widely depending on the temperature and humidity in your kitchen but will typically take around 1 1/2 to 2 hours)
When the dough is almost done rising, preheat the oven to 350°F
Make an egg wash by beating the egg and water (or milk) together well until it is a homogenous liquid.
1 egg, 15 ml water
Using a soft pastry brush, gently brush the tops of the loaves with the egg wash being careful not to deflate the dough.
Bake the loaves in the pre-heated oven for about 35 minutes or until the tops are golden brown and the bread is baked through (or to an internal temperature of ~185°-195°F). If the top starts to brown too quickly/get too dark, loosely tent foil over the loaves.
Remove from the oven and allow to cool in the pans for about 10 minutes, remove from the pans and transfer to a wire rack to cool completely before slicing and serving.