Place the daikon, carrots and cabbage in a heatproof bowl. In a small saucepan, combine the remaining pickle ingredients, stirring to dissolve the sugar. When it simmers, remove from heat and pour the liquid over the vegetables. Cool to room temperature
Preheat the oven to 300°F.
In an oven-safe braising pot, combine the pork belly, pork shoulder, spices, soy sauce, fish sauce, brown sugar, and enough water to come at least halfway up the sides of the meat.
Cover tightly with a lid and braise for 3-4 hours, until the meat is very tender. Remove the meat from the sauce and shred, adding sauce as necessary to moisten.
Place the rice, 2 cups of water and salt in a small saucepan. Bring to a simmer, reduce heat to low, cover and cook until the grains are tender, about 20 minutes.
In a small saucepan, heat the water and sugar for the salad dressing, stirring to dissolve the sugar. Add the remaining ingredients and chill the dressing.
To serve, divide the rice and pork stew between bowls. Top with pickles, cucumbers, jalapeños, carrots and herb sprigs. Serve the dressing on the side.