In a small bowl, combine the potato starch and 1/4 cup (60 milliliters) water. Set aside.
In a large nonstick skillet, heat the vegetable oil over medium-high heat. Add the pork and cook, stirring often, until browned on all sides and some of the fat has rendered, 6 to 7 minutes. Add the onions, garlic and ginger, and cook, stirring occasionally, until the onions have softened, about 5 minutes. Add the potatoes, zucchini and radish, and cook, stirring occasionally, until the radish and potato start to turn translucent, 5 to 6 minutes.
Stir in the black bean paste, brown sugar, salt, and pepper to taste. Add 3 cups (720 milliliters) water and mix well. Simmer gently for 3 to 4 minutes. Stir the potato starch mixture, then add it to the skillet and mix well. Simmer, stirring frequently, until the vegetables are cooked through and the sauce has thickened, 10 to 12 minutes more.
Meanwhile, cook the noodles according to the package instructions (usually 5 to 7 minutes). Drain, rinse well and drain again. Divide the noodles among four to six large bowls. Spoon the vegetable mixture on top of the noodles. Garnish with cucumbers and sesame seeds, and drizzle with sesame oil.
*For even cooking and a nice presentation, cut all the vegetables into uniform 1/2-inch dice. **Do not substitute Chinese black bean sauce here, as it is completely different.
Recipe courtesy of Judy Joo