Add the olive oil to a large dutch oven or another large oven-safe pot over medium-high heat.
When the oil is hot, add the onions along with a pinch of salt and sauté, stirring frequently, until translucent, 3–4 minutes.
Add the carrots, sweet potatoes, smoked paprika, and another pinch of salt to the pot. Continue to cook, stirring frequently, until the veggies start to brown, about 5 minutes.
Add 1 cup of the vegetable broth to the pot and stir, scraping up any browned bits on the bottom of the pot.
Bring to a boil and then reduce heat to medium-low. Cover and simmer until the sweet potatoes are tender, 5–6 minutes.
Stir the Swiss chard, frozen peas, and chickpeas into the pot, cooking until peas are warmed through and Swiss chard has wilted, 2–3 minutes.
Add the flour to the pot and cook, stirring constantly, for 1 minute. Stir in the remaining vegetable broth. Increase the heat to medium and return to a boil.
Reduce heat to medium-low and simmer until the filling has thickened. Season to taste with additional salt and black pepper. Remove from the heat.
Roll out the puff pastry on a lightly floured surface until it is big enough to cover the pot. Drape the puff pastry over the pot and cut a few slits in the center so that the steam can escape as it cooks.
Bake until the puff pastry is lightly golden and the filling is bubbling, 30–35 minutes. Let cool for a few minutes before serving.
As an alternative to baking the filling in one big pot, you can divide it among smaller oven-safe dishes for a portion-controlled, single serving option. These might bake faster, so start checking them at the 20 minute mark.