Stir sourdough starter together with maple syrup, warm water and milk. Beat in the egg, and set the liquid ingredients aside while you prepare the dry ingredients.

Dump the flours into the mixing bowl of a stand mixer, whisk in the salt. Equip the stand mixer with a dough hook, and pour the liquid ingredients into the dry ingredients. Mix the ingredients together on low speed in the mixer for 8 to 10 minutes, stopping the mixer from time to time to scrape the sides of the bowl, or until the dough is uniformly pliable.

Transfer the dough to an oiled bowl, cover it tightly with plastic wrap, and allow it to rise until doubled in bulk - about 6 hours.

Line a 9-inch by 13-inch baking dish with parchment paper.

Punch down the dough, and separate it into 12 pieces of the same size. Roll the pieces of dough into round little balls, and set them into the baking dish. Cover the baking dish with a damp tea towel, and allow the dough to rise until doubled in bulk once more - about 2 hours.

Heat the oven to 375 F.

Make the glaze by whisking cream with 1 tablespoon maple syrup.

Uncover the rising dough, brush them with the maple and cream glaze, and transfer the dish to the oven and bake them about 15 minutes or until golden brown and fragrant. Remove them from the oven. Place a damp tea towel over the baking dish, and allow the rolls to cool. Uncover the rolls, and serve.