Remove brisket from package, rinse and pat dry; cover both sides with dry rub and let sit 30–60 minutes.
Cut onion into eighths and set out remaining ingredients.
Add olive oil to the pot and preheat Ninja Foodi on Sauté Hi.
Rub dijon mustard on both sides of the brisket and resprinkle with dry rub.
Add brisket to the preheated pot and sear all sides until browned, about 3–5 minutes per side; remove and set aside.
Turn off Sauté. Pour in apple cider vinegar, beef broth, water, worcestershire sauce and liquid smoke; scrape browned bits, add beef bouillon base and stir, then add onions.
Place the low rack in pot and set the brisket fat side up on the rack so it hovers above the liquid and onions.
Set Foodi to Pressure Cook on Hi for 1 hour 15 minutes; allow a 20 minute natural release, then remove lid.
Set brisket aside. Pour pot liquid into a medium stove pot, remove and discard onions with a slotted spoon, add 1 cup BBQ sauce and simmer to reduce.
Baste brisket with BBQ sauce, return to Foodi and Air Crisp at 199°C for about 10 minutes; check, flip and baste, then Air Crisp up to another 10 minutes to desired sear.
Remove brisket to a cutting board and let rest 10–15 minutes to allow juices to redistribute.
Slice brisket across the grain, serve on buns with the reduced pan sauce and additional BBQ sauce, and a side of coleslaw.
Tips
Trim excess fat to about 1/4 inch and apply rub at least 30 minutes before cooking.
Check searing frequently during Air Crisp to avoid over-charring; 390°F crisps quickly.
Let brisket rest 10–15 minutes to redistribute juices, then slice thin across the grain.