Bring a large pot of salted water to a boil. Add the vermicelli and cook until al dente. Drain and toss with the 1 teaspoon of olive oil while still hot. Let cool for 20 minutes.
Heat the remaining 3 tablespoons oil in a large skillet over medium-high heat. Add the hen pieces and onion and cook, stirring occasionally, until browned. Add the tomato, water, peas, ginger, turmeric, pepper, parsley, bay leaves, saffron, and chickpeas and cook, stirring occasionally, until the sauce is reduced by 1/3, about 45 minutes.
Spread the vermicelli on a large platter. Pour over the some of the sauce and gently mix. Top with the hens and chickpeas. Add remainder of sauce, as desired, and serve.