Combine oil, cinnamon, curry powder, cumin and ground chili in a large skillet. Cook, stirring often, over medium heat until spices are hot and very fragrant, 2-3 minutes. Add chicken and cook, stirring occasionally to break up the meat. Add onion, garlic and ginger and stir. Add chickpeas and spinach and stir again. Add salt and fresh pepper to taste. Cook until nearly dry, then cool to room temperature. Remove cinnamon stick and discard.
In a food processor, combine flour and salt; pulse to distribute the salt. Add oil and pulse until it has the texture of wet sand. With the blades running, drizzle ice water through feed tube until the dough just forms a coherent mass. Wrap dough in plastic wrap and refrigerate.
Heavily flour a dry work surface. Cut dough in quarters. Working with one ball at a time, roll ball into an 8" circle. Cut in half. With a fingertip or pastry brush, spread water along the cut edge. Fold the half-circle so the cut edge overlaps itself to form a seam, and the whole thing forms a cone (the center of the cut edge forms the tip of the cone). Pinch the seam tightly. Stuff with about 2 tablespoons of filling, or until nicely full. Wet the remaining exposed edge of the dough, and crimp closed. Repeat with remaining dough to form 8 samosas. (Samosas can be frozen at this point for up to a month; fry while still frozen.).
Heat 1 qt vegetable oil in a pot to 360°F Fry in batches until golden and puffy, about 8 minutes. Drain on paper towels. Sprinkle with salt and serve hot.