Four to twelve hours before starting the dough, feed your starter so it is nice and active (bubbly).
In a large bowl, mix together flour, honey, melted butter, and sourdough starter.
Slowly add water and mix until a ball forms.
Cover and allow to ferment for 12-24 hours for the most benefit from the sourdough. (Skip if you want to bake right away)
The next day, preheat oven to 375 degrees.
Uncover the dough, sprinkle with salt, baking soda, and baking powder.
Knead dough together to make sure all the ingredients are incorporated well, about 3-5 minutes.
Place dough on the floured surface and roll out into an even rectangle that is about 1/4 to 1/2 inch thick.
Brush the dough with butter, then spread the raspberry jam over the dough, leaving about 1/4 inch of space from the ends.
Starting from one side and working down the edge, roll up the dough as tightly as you can. Pinch the ends of the dough to the roll to help keep it together.
Slice into equal rolls. Usually I slice it into about 10-12 rolls.
Place in a greased or parchment-lined baking dish or cast iron skillet.
Pour remaining butter over the rolls as evenly as possible and sprinkle with brown sugar.
Place in oven and bake for 20-25 minutes until the rolls start to turn golden.
While the rolls are baking, make icing by whisking together powdered sugar, milk (or water), and vanilla extract.
Allow sourdough raspberry rolls to cool, then drizzle with icing.