Puree the raspberries using a blender or food processor. Reserve all juices if using thawed frozen raspberries.

In the bowl of a stand mixer, mix the flour, milk, sourdough starter, pureed raspberries, eggs, sugar, salt, optional freeze-dried raspberries, and optional food coloring on low speed for 3-4 minutes until incorporated.

Add the softened butter and mix on medium speed for 10 minutes until smooth and elastic. If necessary, add additional flour in increments until dough comes together.

Transfer the dough to a lightly greased bowl, cover, and let rise for 4-6 hours, performing stretch and folds every 30 minutes. Dough should double in size.

Cold proof the dough in the refrigerator overnight (8-12 hours).

Roll the chilled dough into a 24-inch by 14-inch rectangle, approximately ¼ inch thick. Wrap in plastic wrap and freeze for 1 hour.

Remove from freezer, trim edges for a clean rectangle, and slice into six 4-inch by 14-inch rectangles. Cut each rectangle into triangles.

Roll each triangle into a tight croissant shape and transfer to a lined baking sheet. Cover loosely and let rise until doubled in size (2-5 hours).

Heat frying oil to 375°F. Carefully add croissant donuts to the oil, cooking for 1 minute on each side until golden brown. Transfer to a rack to cool.

Toss cooled donuts in granulated sugar until evenly coated.

Poke a hole in the bottom of each donut for filling. Pipe pastry cream and raspberry jam into each donut, topping with more pastry cream if desired.