Add all of the dry rub seasoning and BBQ sauce ingredients into the pot and mix well with the broth to create a sauce. (please see the notes below)
Nestle the meat into the sauce mixture and use a cooking spoon to spread the broth over the meat.
Lock the lid onto the pot.
Set to "Manual" and cooking time to "70" minutes. When the cooking cycle is done and beeps, let the pressure release naturally for 10 minutes then turn the PRESSURE RELEASE valve to the VENT position.
Unlatch the lid and open the instant pot.
Skim the excess surface fat from the sauce.
Use a meat fork or two regular forks to transfer the brisket to a cutting board to pull it apart and shred. This is safer than pulling it apart in the instant pot which can be hot.
Place the shredded meat back into the pot. Then turn the instant pot to the "saute" setting and cook for about 8-10 minutes, or until the sauce looks like a loose, wet BBQ sauce.
Turn off the "saute" function. Remove the meat from the instant pot and transfer the sauce into the bowl. The sauce and meat taste great together but are best stored separately as to keep the meat from getting soggy.
Serve the meat on a bun and add coleslaw. Add additional sauce as desired.
Briskets come in two basic cuts. Choose the "flat cut" because it is less fatty than the "point cut".
If your brisket is too big, just cut in half until it fits comfortably in the pot.
Don't have liquid smoke? Just skip it :)
Optional step for tender meat: You can place the brisket in a large, heavy-duty Ziploc bag. Rub the meat with dry rub seasoning and marinate for at least 2 hours or up to overnight to provide flavor and help tenderize the meat before adding into the pot, mix with broth, and the BBQ sauce ingredients.