1. Bring broth, 4 cups water, squash, potatoes, Swiss chard stems, thyme, and salt to a boil in stockpot. Cover, reduce heat to medium, and cook 5 minutes. Add Swiss chard leaves and corn, and cook 3 minutes more. Drain vegetables, and reserve broth. Measure broth, and add enough water to make 7 cups liquid. Transfer vegetables to large bowl, and stir in chickpeas.
2. Wipe out stockpot, add oil, and heat over medium-high heat. Add onions, and sauté 7 to 10 minutes, or until beginning to brown. Sprinkle with flour and garlic, and cook 1 minute. Add reserved 7 cups broth liquid, and cook 5 to 7 minutes, or until sauce thickens, stirring constantly. Stir in almond milk. Stir sauce into vegetable mixture, and season with salt and pepper, if desired. Cool. (If making ahead, transfer filling to bowl, cover, and refrigerate up to 2 days.)
3. To assemble pot pie: Preheat oven to 375°F. Pour filling into deep 13- x 9-inch baking dish.
4. Gently roll out puff pastry sheet to size of baking dish on lightly floured work surface. Transfer to baking sheet lined with parchment paper, and chill 30 minutes.
5. Place chilled puff pastry sheet over filling on top of baking dish, and press around edges to seal. Use tip of sharp paring knife to score 4 rows of diagonal incisions into puff pastry (without cutting completely through), alternating directions with each row.
6. Bake 30 minutes, or until top crust is golden brown. Cool 10 minutes before serving.