Combine all the ingredients for the peanut sauce in a medium mixing bowl or large measuring cup and whisk until well combined.
Place the shredded chicken meat and chopped peanuts in a large bowl and pour about half the peanut sauce over it. Mix until very well combined.
Make sure that you have all your other filling ingredients prepped, ready and handy before you start rolling.
Fill a large shallow bowl with lukewarm water. Try and find one in which you can pretty much fit an entire disc or at least half of it and rotate it.
Quickly dip a rice wrapper in the lukewarm water. These wrappers are extremely delicate and only require a very quick dip to soften up. Do not leave them in there for too long because they will become way too soft, break down and become impossible to roll.
The wrappers should still be somewhat firm as you take them out of the water; once it lays on the wet prepping surface, it will continue to absorb water and will become soft and sticky in no time. Always build your spring rolls a non-porous surface such as a large ceramic plate or a glass, stone, smooth plastic or ceramic cutting board, and make sure to keep that surface wet all the time.
Lay the ingredients at the top third of the rice paper, starting with a few spinach leaves (the leaves will act as barrier and protect the fragile rice wrappers against eventual tears), followed by a few pieces of carrots, cucumber and green onions. Top with a few tablespoons of rice and finally, a few tablespoons of the peanut chicken mixture. Be careful not to over-stuff the rolls and make sure to leave about an inch on both sides so you can tuck them in later.
Very delicately pull the edge of the rice wrapper away from the work surface and fold it over the filling. At the same time, use your thumbs to gather and tuck the filling under the wrapper.
Slowly start to roll towards you while continuing to hold and tuck the filling with your fingers. Roll about one complete rotation, then fold in the sides. The rice wrappers are very sticky, so they should stick almost instantly and hold in place just fine. Continue to roll until the wrapper ends, while always tucking and guiding the filling with your fingers.
Continue making more spring rolls until you run out of ingredients; keep the finished rolls on a non-porous surface while you work on the others. Do not let the rolls touch otherwise they will stick together and tear when you try to take them apart.
Slice the finished rolls in half, on a slight diagonal, and serve promptly with the rest of the peanut sauce.
Spring rolls are at their best when fresh, but leftovers can be kept for up to 24 hours if wrapped tightly and individually in plastic film.