Combine the sourdough starter, water, and flour in a bowl. Cover and proof at approximately 78°F (26°C) for 8-10 hours, until at least doubled in size.

In the bowl of your stand mixer fitted with a dough hook, combine all ingredients except for the butter. Mix into a shaggy dough for 1-2 minutes. Cover and let rest/autolyse for 30 minutes.

After the autolyse, continue mixing for 5-10 minutes until the dough starts to pull away from the sides of the bowl.

Gradually add the cubed, softened butter while continuing to mix at medium speed for 10-25 minutes. Perform the window-pane test to ensure dough readiness.

Transfer the dough to a clean bowl, cover, and let proof in a warm place (75-78°F/24-26°C) for 6 hours. If you don’t have a dough proofer, place the dough in the oven with the light on and the door slightly open.

After 6 hours, transfer the dough to the fridge to cold-proof for 6-8 hours.

Divide the dough into 15 equal pieces (60 g each) and roll them into seamless rounds. Place the shaped donuts on baking trays lined with floured parchment paper squares (5 in/12 cm). Loosely cover the trays with plastic wrap.

Proof the donuts in the oven with the light on and the door slightly open (or in a proofer box) for 10-14 hours until they’ve doubled in size.

In a stainless steel pot, combine sugar and water. Bring to a boil over medium heat without stirring to prevent crystallization.

Let the mixture boil until it turns a light golden color, about 6 minutes. You can gently swirl the pan and use a wet pastry brush to wash down the sides if needed.

Lower the heat and add cubed butter, stirring to combine.

Gradually add the whipping cream, stirring between additions, and allow the caramel to boil for about 1 minute.

Remove from heat and stir in the sea salt. Transfer to a bowl and let cool at room temperature.

Once the donuts have doubled in size, use a floured 1.2 inch (3 cm) cookie cutter or the back of a large piping tip to remove the centers.

Heat oil in a Dutch oven or heavy-bottomed pot to 355°F-365°F (180°C-185°C), using a thermometer to maintain temperature.

Carefully lower the donuts into the hot oil, frying them for about 1.5 minutes on each side. Remove with a metal slotted spoon and transfer to a cooling rack lined with paper towels.

Repeat with remaining donuts and donut holes.

Dip each donut into the caramel glaze and, if desired, top with crushed gingerbread cookies for added texture and flavor.