Put the pork in the freezer while you prepare the rice. Put the rice in a medium saucepan and add 2 cups water, the lemon zest and 1/2 teaspoon salt; bring to a boil. Stir, then cover and reduce the heat to low. Cook until the water is absorbed, about 10 minutes. Turn off the heat and let stand 10 minutes. Fluff the rice with a fork.
Meanwhile, cut the pork into 1 1/2-by-1/2-inch strips. Season with salt and pepper. Heat 2 tablespoons vegetable oil in a large nonstick skillet over high heat until very hot. Add half the pork and cook until browned, about 2 minutes per side. Remove to a large bowl; repeat with the remaining pork.
Add another 1 tablespoon vegetable oil to the skillet over medium heat. Add the haricots verts, 1/4 teaspoon salt and 1/3 cup water; cook, stirring, until the water evaporates and the haricots verts start browning, about 6 minutes. Add to the pork.
Add the remaining 1 tablespoon vegetable oil, the garlic, jalapeno and ginger to the skillet and cook, stirring, until golden, 1 minute. Add the brown sugar, fish sauce and 1/4 cup water; cook until the sauce is thick and bubbling, 1 to 2 minutes. Add the pork and haricots verts to the sauce and toss until glazed, about 1 minute; season with salt. Serve the stir-fry with the rice; top with cilantro and/or mint.