Combine the cooled pumpkin spice latte, bread flour, and active sourdough starter in a large bowl and mix until no dry flour remains and the dough is shaggy. Cover and rest for 1 hour.
Add the salt, vanilla extract, and pumpkin spice to the rested dough with wet hands, along with the reserved splash of latte to help the additions work through evenly. Squeeze and fold the dough until everything is fully incorporated and you cannot feel any undissolved salt.
Perform three sets of stretch and folds spaced 45 minutes apart. For each set, pull the edge of the dough up and fold it into the middle, working around the bowl about six times, then flip the dough over onto itself so the seam is underneath and push and tuck the edges until the ball is taut.
Cover and bulk ferment at room temperature for 6 to 8 hours, until the dough has increased 50 to 70 percent, feels smooth rather than sticky, releases from the side of the bowl, shows bubbles on the surface, and springs back slowly when poked. The sugar in the latte speeds fermentation, so begin checking at 6 hours.
Turn the dough onto a lightly floured surface, pre shape into a loose round, and rest uncovered for 20 to 30 minutes.
Shape the dough into a tight boule or batard, rolling it up firmly to build surface tension, and place it seam side up in a banneton lined with a cotton liner.
Cover and cold proof in the refrigerator for 14 hours.
Place a Dutch oven with its lid into the oven and preheat to 450 degrees Fahrenheit for at least 45 minutes.
Turn the cold dough out onto a piece of parchment, score the top with a lame, and lower it into the preheated Dutch oven using the parchment. Cover with the lid and bake for 45 minutes.
Remove the lid and bake for another 5 to 10 minutes, until the crust is deeply golden and the internal temperature reaches 205 degrees Fahrenheit. Tent loosely with foil if the crust darkens too quickly.
Transfer the loaf to a wire rack and cool completely for at least 4 hours before slicing. Cutting early will give you a gummy crumb.