Puree the raspberries using a blender or food processor, reserving all juices from thawing if using frozen.

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

Add softened butter and mix on medium speed for 10 minutes until smooth and elastic. Add additional flour in increments if dough isn't coming together.

Transfer the dough to a lightly greased bowl. Cover and let rise for 4 to 6 hours, performing 2-3 sets of stretch and folds every 30 minutes.

Transfer the dough to the refrigerator to cold-proof overnight (8-12 hours).

Roll the chilled dough into a 24-inch by 14-inch rectangle that is ¼ to ⅓ inch thick. Wrap in plastic wrap and place in the freezer for 1 hour.

Remove the dough from the freezer and on a lightly floured surface, re-roll to ensure it is ¼ to ⅓ inch thick. Trim edges to create a clean 24-inch by 16-inch rectangle. Slice into six 4-inch by 14-inch rectangles.

Cut each rectangle into two triangles by slicing from one corner to the opposite corner to create 12 triangles.

Roll each triangle into a croissant shape, tugging on the corners to lengthen slightly.

Transfer the croissant donuts to a lined baking sheet. Loosely cover and let rise until doubled in size (2-5 hours).

Heat frying oil in a heavy-bottomed pot to 375°F. Fry the donuts, two to three at a time, for 1 minute on each side until golden brown. Cool on a rack.

Toss the cooled donuts in granulated sugar until coated.

Poke a hole in each donut and use a piping bag to fill with custard and raspberry jam.