Heat the olive oil in a large skillet over medium-high heat until shimmering.
Add the chopped onion and sauté 3–4 minutes until softened, then stir in the minced garlic, curry, thyme, anchovy fillets, lemon zest, 1/2 teaspoon salt, and a pinch of black pepper; cook, stirring, until onion is tender and mixture is fragrant and slightly golden.
Reduce the heat to medium-low and add the chickpeas and brown sugar; cook, stirring occasionally, until the chickpeas begin to brown, about 8 minutes.
When the chickpeas start to dry, add the chicken broth and the juice of half the lemon; simmer and reduce for about 6 minutes, then remove from 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, add the spinach and chopped parsley to the chickpeas and toss until the spinach wilts.
Add the drained orecchiette to the skillet and toss thoroughly to coat the pasta with the chickpea mixture; adjust seasoning with salt and pepper to taste.
Serve into bowls, sprinkle each portion with zaatar, and drizzle a little extra olive oil if desired.