Heat the olive oil in a large skillet over medium-high heat.
Add the chopped onion and cook 3–4 minutes until softened, then stir in the minced garlic, curry powder, thyme leaves, anchovy fillets, lemon zest, 1/2 teaspoon salt and a few grinds of black pepper; cook, stirring constantly, until the mixture is fragrant and golden.
Reduce the heat to medium-low and add the drained chickpeas and brown sugar; cook, stirring occasionally, until the chickpeas begin to brown, about 6–8 minutes.
When the chickpeas start to dry, pour in the chicken broth and the juice from half the lemon; simmer and reduce for about 6 minutes, then remove from the heat and set aside.
Meanwhile, bring a large pot of salted water to a boil and cook the orecchiette until al dente according to package instructions; drain and reserve.
Return the skillet to low heat if needed and add the spinach and chopped parsley to the chickpeas; stir until the spinach wilts.
Add the cooked orecchiette to the skillet and toss well to coat the pasta with the chickpea mixture; adjust seasoning with salt and pepper to taste.
Divide among four plates or bowls, sprinkle each serving with zaatar and drizzle a little olive oil before serving.