Soba noodles are made from fiber-rich buckwheat flour, which keeps you full longer. If you can't find Chinese broccoli, use other leafy vegetables such as mustard greens.
Prepare an ice-water bath. Bring a large pot of water to a boil. Cook noodles until al dente. Drain, and transfer to ice-water bath. Drain, and transfer to a large bowl. Toss with 1 tablespoon oil.
Heat remaining 2 tablespoons oil in a medium Dutch oven or a large pot over medium-high heat. Cook ginger and garlic until fragrant, about 1 minute.
Add stock and water. Bring to a boil. Stir in Chinese broccoli, and simmer until crisp-tender, 3 to 4 minutes.
Reduce heat to low. Stir in pork and soy sauce. Cook until pork is just cooked through, about 1 minute.
Divide noodles and soup among 4 bowls. Garnish with chile and lime wedges. Serve immediately.