Melt the butter in a large Dutch oven over medium-high heat. Add the onion, sugar, and salt and cook until the onion is softened and just starting to brown at the edges, about 5 minutes.

Stir in the garlic, paprika, saffron, ginger, and cumin and cook until fragrant—keep the mixture moving for about 30 seconds to prevent the spices from scorching.

Stir in the chickpeas, potatoes, tomatoes with their juice, zucchini, and broth. Bring to a simmer, then reduce the heat to medium-low and cook, stirring occasionally, until the potatoes are tender when pierced with a fork, 20 to 30 minutes.

Using a wooden spoon, mash some of the potatoes against the side of the pot to release their starch and thicken the broth.

Remove the pot from the heat and stir in the parsley. Season with salt and pepper to taste and serve hot with lemon wedges for squeezing over.