Preheat the oven to 350°F.
Grease your 3.75-quart STAUB Cast Iron Pumpkin Cocotte (or a 9″ cake pan).
In a small saucepan, combine all ingredients for the pumpkin-caramel sauce, except the vanilla extract. Bring it to a low simmer, and let it bubble gently for 3–5 minutes, until it’s incorporated and slightly thickened. Remove from heat, add the vanilla extract, and set aside.
In a large bowl, stir in 1 cup of all-purpose flour, along with the active dry yeast, warm water, warm milk, egg, white sugar, butter, salt, and vanilla extract until combined.
Add the remaining 2 ½ cups of all-purpose flour. Knead until the dough comes together. Cover it with plastic wrap, and let it rise in a warm place for 30 minutes.
Turn dough out onto a lightly floured surface, and punch down gently to deflate. Divide dough into small or medium balls.
Dip each ball of dough into the pumpkin-caramel sauce, and then place them in a layered arrangement in your greased pan.
Cover it with plastic wrap or a damp cloth, and let it rise for about 45 minutes, until it’s almost doubled in size.
Bake at 350°F for 30 minutes, until it’s golden brown.
Invert bread onto a large plate, and spread remaining pumpkin-caramel sauce over the bread while it’s still warm. Let it cool slightly before serving.
