Here are the directions for ribs that I have posted before and they can definitely be used for a shoulder/butt.
If brining use these ratios for an appropriate amount of liquid to cover the ribs in a gallon ZipLoc bag and make sure to completely dissolve the sugar and salt:
1 cup of kosher salt
1 cup of turbinado sugar
1 gallon H2O
After brining, dry the ribs as thoroughly as possible with paper towels and allow to come to room temperature on a wire rack on a half sheet pan.
Dry Rub…of course there are myriad permutations, but here is what I ran with on these:
8 TSP Dried, Evaporated Cane Juice
3 TSP Kosher Salt
3 TSP Sweet Paprika
1/2 TSP Granulated Garlic
1/2 TSP Onion Powder
1/2 TSP Yellow Mustard Powder
1/2 TSP Finely Ground Telicherry Pepper
1/2 TSP Szichuan Peppercorns
When the ribs are at room temp, apply a fairly thick coating of the rub on all sides. When liquid starts to appear on the sheet pan, it is time to hit the smoker. Since you are the proud parent of a new Weber, I will give the instructions for how I use mine.
Approximately 30 to 40 minutes before you intend to put the ribs on, start some hardwood lump charcoal in your chimney. About half full give or take…this will require trial and error based on your brand and chunk size. When the coals have all started, place them on one side of the grill in a nice mound as close to the wall of the kettle as possible. Keep the bottom vent 100% open and play with the top between 25 and 50% to keep temp around 225 to 250 deg F. As for smoke wood, I use pecan and pecan shell from my parent’s trees. For best results, IMHO, find some pecan/hickory/apple smoking chips and make several foil pouches filled with about a half to full cup worth. Make sure they are very tightly wrapped and poke a couple of holes in each of them. When the coals ash over, place the foil pouch directly on them and wait for smoke to appear. It might not seem like very much, but once the lid is closed, you have a smoker. Throw the ribs on as far away as possible from the fire.
Here is the tricky part…maintaining a decent temp and keep the smoke going uninterrupted. I usually put a new foil pack on every 15 minutes for two hours. That is about as much smoke flavor as is needed for ribs. After that, just add charcoal to keep the heat going. Based on wind, ambient temp, your internal temp, etc…I would say look at six hours for good results. If you don’t want to fuss with all of that, you can of course put them on your wire rack on the sheet pan and put in a 225 deg oven for four hours post smoking.
Mopping:
I get a good glaze on the ribs by applying a mop sauce vs. a traditional BBQ sauce and in the end no sauce is needed. If you want to go this route, mop the ribs every 15 minutes after the smoke has been halted.
Mop Sauce:
1 Cup Apple Juice
1/2 Cup Turbinado Sugar
2 TBS Of Left Over Rib Rub
2 TBS Worchestershire Sauce
2 TBS Apple Cider Vinegar
Combine all ingredients in a sauce pan and heat to dissolve sugar.