Preheat the oven to 400 degrees.
On a cookie sheet, combine the squash, chickpeas, shallots, salt, cinnamon, honey, and nutmeg. Drizzle with olive oil and toss with your hands so everything is well covered with spices and oil. Roast in the oven for 20-25 minutes, until squash is caramelized but not falling apart.
On another cookie sheet, drizzle the sprouts with oil and season with salt. Roast these at the same time as the squash for about 15 minutes, redistributing occasionally until they are brown and crispy all over.
While the veggies are roasting, pulse the ginger, garlic, shallot, and walnuts together in a food processor until finely chopped. Add the honey, mustard, lime juice, vinegar, salt, and cayenne. Drizzle in the olive oil until the dressing consistency is in between that of vinaigrette and that of a pesto—you don’t want it too thin.
Bring a large pot of salted water to a boil and cook the orzo according to package directions until al dente. Drain and toss the warm pasta with the veggies and the dressing. Taste for seasoning and add any salt as necessary. Serve the pasta warm or at room temperature.