Bear with my as I try to describe this issue. After coming to a stop from medium to high speeds (35mph+) my truck does makes a quick jolt and along popping sound. The “pop” sounds like someone striking an anvil with a hammer. The sound and jolt occurs only after a full stop, and after releasing the brake pedal. I have noticed that if I make a more gradual brake, the pop/jolt does not happen. It tends to happen when braking harder, and when my truck is facing more downhill.
I am trying to get a general idea of where the issue is, be it the brakes, transmission, or suspension.
Something is broken or wore out. Get the front suspension and brakes looked at soon. Before that jolt/pop drops the whole front end on the ground, or sends you screaming through a busy red light.
I would suspect the rear leaf springs are binding up from rust and wear. I’d follow @PvtPublic’s advice and have the front end and brakes looked at, too.
it might help if you told us if the sound you here is near the front , middle, or back. it could be something as simple as your exhaust being loose and slamming back and forth or what Tester said.
Front end suspension: I have inspected this and there is no play in the front suspension components. Most I have seen is some cracked rubber in some bushings, but no play. It’s pretty solid
Brakes: front brake hardware seems solid. Brake wear is even and there doesn’t seem to be any issue with calipers binding. Rear hardware was all recently reinstalled. The sound occurred before and after this install
Driveshaft: I haven’t inspected it thoroughly yet, but reading through these suggestions makes me think the issue could be there. Tester provided a solution that is pretty easy to attempt. I will check the u-joints as well.
As far as the location of the sound, it is hard to tell exactly where it is coming from while driving. It seems like the front to me, but I’ll have to have someone else drive it to be sure.
I forgot to mention as well that the leaf springs look good as well. Just some surface rust however the driver side rear does have a left lean. Even though the leaf spring itself looks like it’s in good condition, it could also a part of the issue.
I own a similar truck. The slip yoke bump, in my experience, is most noticeable when the trans downshifts from third to second.
The trucks are pretty prone to lean on the left due to the gas tank being on that side, so that may or may not be normal.
A couple of other areas to check are motor and trans mounts, although I’d think they’d be more prone to making noise on an abrupt acceleration rather than braking, as would the drive shaft.
Tailgate. My 07 Silverado Classic does the same thing, also when taking off too fast. The plastic bushings on the tailgate latch wear out, then the tailgate gets about 1/4"+ of play.