Place pumpkin purée, water, salt, yeast, and honey in a large mixing bowl. Mix together well.
Add I cup of flour and thoroughly combine, repeat with 2 remaining cups of flour.
Reach into the bowl and mix well with your hands. Knead dough until it is smooth and elastic.
Tidy dough into a ball and cover the bowl with plastic wrap. Let rise 12 hours (up to 18 hours) until the dough has more than doubled and bubbles can be seen on the dough surface.
Carefully remove dough from the bowl and place onto a clean work surface.
Grab the side of the dough farthest away from you, stretch up (about 3 times the height of the dough) then fold over the dough. Repeat on the right side of the dough, the side closest to you, and finally the left side.
Flip over the dough ball so that the smooth side is on top. Cup your hands around the ball and slide it slightly forward on the countertop. Rotate, and repeat until the dough is a neat ball.
Carefully place the dough ball (smooth top facing downward) in a well-floured *banneton. Alternatively, line a medium bowl with a well-floured tea towel and place the dough ball in there.
Cover and let rise until doubled, approximately 1-2 hours.