Before you begin: This is an overnight dough which takes approximately 12-18 hrs to rise @ 68 F. Start the night before, in the evening, and plan to bake the following day. See my note below on how to speed up the rise time in chilly weather. Enjoy!

1. Warm the milk in a small saucepan or microwave and set aside. Note: if you use cold milk straight from the fridge, the dough will take longer to rise.
2. In the bowl of a stand mixer, combine the flour, sugar, and salt with the paddle attachment. Add the softened butter, cube by cube, with the machine running. The goal is to evenly disperse the butter throughout the flour; rub any large pieces together with your fingertips. 
3. Add the warm milk, starter, and egg to the bowl. Mix for 1 minute to combine. With your hands, work the dough into a rough ball incorporating any dry bits of flour at the bottom. Cover the bowl with plastic wrap and rest for 30 minutes.
4. Meanwhile, soak the chopped raisins in the vanilla extract. 
5. After the dough has rested, add the raisins (and any liquid), cinnamon, and pumpkin pie spice to the bowl.
6. Using the dough hook, mix on medium-low speed, about 3 on a KitchenAid for 8 minutes. If the dough starts to climb up the side of the bowl, stop the machine and push it back down. The dough will be smooth and supple when finished. It should not stick to your hands. If it does, add a sprinkle of flour.
7. Cover the bowl with plastic wrap and let rise overnight at room temperature (about 68 F) for 12-18 hours. The dough is ready when it has tripled in size. Optional Step: about 1 hour into the bulk rise, I like to do 1 set of stretch and folds. I’ll do another set about 1 hour later. This technique will speed up the bulk rise time and the overall volume of the baked buns. **See note below. 
8. The following day, generously coat the bottom and sides of a 9×13-inch pan with butter.
9. Remove the dough onto your work surface- no need to flour the surface first. Gently shape the dough into a log. Cut into 12 equal pieces, about 92 g ea.
10. To shape into balls: working with one piece of dough at a time, fold the sides over towards the center. Flip it over, keep it on the counter, and roll it into a ball with the palm of your hand. Place the balls into the pan, evenly spaced, 3 across and 4 down.
11. Cover the pan with plastic wrap or a damp kitchen towel, and let rise at room temperature until the dough has doubled in size. This can take up to 2-3 hours at 68 F. Personally, I like to use the proofing box or oven trick at this point (again, see me note below). The rise will only take about 1 1/2- 2 hours @ 75-80 F. The dough should look very puffy and plump when ready. Do not rush this step; the buns will be dense.
12. While the dough is resting, make the icing for the cross. In a small bowl, whisk the softened cream cheese, butter, powdered sugar, and half-n-half. Add additional liquid as needed; the texture should be thick enough to pipe. Put the icing into a ziptop bag with the tip snipped off, or in a squeeze bottle and refrigerate to firm up before using. You will not use all of the icing. Save the rest for another use.
13. Preheat your oven to 400 F.  Place the dough inside, center rack. Reduce the heat to 350. Bake for 28-30 minutes.
14. Meanwhile, combine the apricot jam and a splash of water in a saucepan.
15. Remove the buns from the oven. Brush the tops with some of the glaze while they’re still hot.
16. When the buns are COMPLETELY COOL, pipe the cream cheese icing on top going in one direction first, and then the other. Do not make an individual cross on top of each as you go- it will drive you crazy.
17. Serve the buns fresh at room temperature.