Cut the brisket into 3 to 4 strips or chunks, depending on the size of your Instant Pot. Liberally salt the meat on all sides.
Prep your smoker according to the manufacturer’s instructions. If you don’t have a smoker, you can skip this step (see Tips below for alternatives).
Smoke the brisket at 225°F for about 30 minutes to infuse it with a subtle smoky flavor. For a stronger smoky profile, extend this step to one hour.
Set your Instant Pot to its high heat sauté setting, add the tallow, and swirl it to coat the bottom of the pot.
In batches, sear the brisket for 2 to 3 minutes on each side, creating a rich brown crust. Avoid overcrowding the pot to ensure even browning.
Once all the pieces are seared, add ½ cup of water to the pot, scraping up any browned bits from the bottom. This step enhances the flavor of the cooking liquid.
Secure the Instant Pot lid, set the vent to sealing, and pressure cook on high heat for 45 minutes.
Allow the pressure to release naturally for 20 minutes before opening the lid.
Remove the brisket and let it rest for a few minutes. Slice it into large pieces for serving or shred it for a tender, pulled-brisket style.