Preheat the oven to 400°F.
Cut the spaghetti squash in half lengthwise. Place the halves face-up on a baking sheet and drizzle with 1 1/2 teaspoons of the olive oil. Season the squash with salt and pepper and slide the sheet into the oven. Roast the squash until tender strands start to pull away, about 40 minutes. Remove the seeds from the squash and set aside.
While the squash is roasting, toast the pine nuts in a medium sauté pan over medium heat. Once pine nuts are golden brown, remove them and set aside.
Make the arugula cream: In an upright blender combine the cashew butter, water, garlic, lemon zest, 1 tablespoon of the lemon juice, tamari, arugula, salt, and pepper. Blend this mixture on high for about 45 seconds, or until totally smooth and fluid. Check the cream for seasoning and adjust if necessary. Transfer the cream to a sealable container and keep in the refrigerator until ready to use.
Return the medium sauté pan with the remaining 1 1/2 teaspoons of olive oil to the stove over medium heat. Add the shallots to the pan and cook, stirring often, until very soft, about 4 minutes. Add the chickpeas to the pan and season with salt and pepper. Once the chickpeas are warmed through, stir in the remaining tablespoon of lemon juice.
To serve, place warm squash halves on plates and gently pull out some strands of "spaghetti" to make a pocket of sorts. Divide chickpea mixture between both squash halves. Drizzle garlicky arugula cream over both servings, and garnish with toasted pine nuts and extra arugula