Heat 2 tablespoons canola oil over medium high heat in a large skillet. Add ginger and shallot and cook until fragrant, about 2 minutes.
Meanwhile, in a small bowl, whisk together soy sauce, rice wine vinegar, and sugar. Add mixture to skillet, then stir in stock and bring to a simmer.
Toss in squash and cook until softened, turning once, for about 8 minutes. Reduce heat to low, cover, and cook for an additional 12-18 minutes, turning occasionally, until squash is tender but not falling apart and sauce has thickened.
While squash is braising, heat remaining 1 tablespoon canola oil in a cast iron skillet over high heat. Add shishito peppers and cook until they start to char, about 6-8 minutes, turning half way through. Add a generous pinch of Kosher salt and remove from heat.
When squash is done, transfer to serving plate and drizzle sauce on top. Top with peppers and serve immediately.