The "trick" you're looking for is a side hop. It's really a variation on a bunny hop.
Basically, you perform a standard bunny hop but when the handlebars and front wheel reach their zenith, you pull the front end over the obstacle while pushing them forward. The forward motion pulls the rear wheel up, as with a standard bunny hop. However, you additionally use your hips and legs to push the rear of the bike over the curb as well.
The video I linked to above gives a good example. The one quibble I have is that he says that it's easier to jump away the side of your forward facing foot. I find the opposite to be true. I find that my rear foot gives me more leverage to push the rear wheel over the obstacle. But really, I can do them both ways. I can just do them higher and farther in my preferred direction.
Side hops are typically done from a trackstand rather than in motion. This is because they are mostly used for trials and executing the trick from a standstill offers more precision and control. Practice from a standstill. Once you get relatively good at it, try doing it while rolling slowly. Then gradually increase speed.
When starting out, practice on flat ground that has some sort of marking on it, e.g., painted lines, different color bricks, chalk lines, whatever. From a trackstand, try to hop from a few inches to the side of the marking onto it. Once you can do that confidently, try hopping from the same starting position, but over the marking. Then try from farther away.
Once you've got that down, add some height in. Stairs are a good place to practice. Once you can hop onto a single stair, find a wide stairway and try to hop all the way to the top of it. If you have to put a foot down, make sure to do it on the higher step. You won't be able to reach the lower step and could tumble down the stairs.
At this point, you're ready to start trying to do it rolling. Go back to your flat ground with markings on it. You'll find that you can't side hop as high or far while rolling. At least, not initially. I can't explain why it's different, but it definitely is. You'll get a feel for it much more quickly though and soon you'll be ready to tackle curbs. Do so slowly at first. You'll probably catch your rear wheel and come to a skidding halt a few times. Once you get it, go faster and faster until it's second nature.
Practice each step in both directions. If you get good at going one direction first, it will be more frustrating to learn to go the other way.
Doing this with a backpack on is nothing. Doing it with a weighted rear end (i.e., panniers) is a whole different ball game. While it may be possible, it would certainly not be easy. You simply don't have the same leverage with the weight on the rear. I would also worry that the jarring of the panniers and rack would ultimately damage them. Racks are not designed to withstand a lot of lateral force. Pannier hooks are also not typically designed for impact forces. If you find yourself having to do this often, you might have to resign yourself to riding with a backpack.