To make the quick-pickled carrots, combine ¼ cup rice vinegar with 2 Tbsp water and the honey or sugar. Add the carrots and stir to combine. Set aside.
To make the dumpling sauce:
Combine ¼ cup soy sauce with the remaining 3 Tbsp rice vinegar, garlic and sesame oil.
Thinly slice half the ginger (a 1-in piece) along with the dark green top of one scallion. Add to the dumpling sauce.
For the shrimp:
If you’re using frozen shrimp, thaw it completely and drain as much water as possible, using a paper towel to pat it dry. Finely chop with a knife, until it’s about the consistency of ground meat. Add to a large mixing bowl.
Mince the white and light green parts of the remaining scallions along with the remaining 1-in piece of ginger and add them to the bowl with the shrimp.
Season with the remaining 1 Tbsp soy sauce and (if using) the sriracha; stir until completely incorporated.
Set a large lidded skillet over medium heat with 1 tsp oil.
When the oil is hot, add the shrimp mixture and spread it in an even layer. Cook undisturbed for 1 to 2 minutes, then stir and cover to let the residual steam finish the cooking.
Drain the quick-pickled carrots.
To serve, wrap the filling in lettuce leaves and serve with pickled carrots, dumpling sauce, and (if using) more sriracha on the side.
If making rice bowls, omit the lettuce and serve over 3/4 cups cooked rice (not included in macros/points).