Thinly slice the pork into strips about 1 1/2 inches long and 1/2 inch wide and set aside
If using pork fat, place a large heavy pot over medium heat and toss in the fat; when it has melted, raise the heat to high. Or, if using vegetable oil, place the pot over high heat, add the oil, and heat until very hot. Toss the shallots and garlic into the pot and stir as they start to soften and change color
Add the sliced pork and stir-fry, using your spatula to separate the pieces and expose all surfaces to the heat, until the pork has changed color. Add the water and then toss in the greens, dill, and chives. Stir to immerse the greens in the water and bring to a boil
Tear 3 of the lime leaves into coarse pieces and add to the pot. Stir to make sure all the ingredients are immersed, then lower the heat and simmer gently, half-covered, for 1 hour. Stir occasionally to make sure nothing is sticking. The dish will cook down, leaving 2 1/2 to 3 cups liquid and very melting greens. Add the fish sauce, stir, and taste for seasonings
NOTE: The stew can be made ahead to this point and set aside until just before you wish to serve it. If leaving for longer than 2 hours, let cool completely, place in a well-sealed nonreactive container, and refrigerate. About 5 minutes before you wish to serve the stew, bring back to a gentle simmer)
Add the chopped scallion greens to the stew, stir, and add the remaining lime leaves. Transfer to a serving bowl and generously spoon so guests can help themselves. Serve as one of several dishes in a rice meal. Invite your guests to begin with a mound of rice on their plates and then top with some stew, or provide small individual bowls for the stew, so guests can eat it on its own or with their rice