Cook pasta until al dente, adding peas in the last few minutes of cooking. Drain and put in a large serving bowl.
Meanwhile, in a small saucepan, bring broth to a simmer. Add leeks and cook until softened, about 5 minutes. Stir in chicken and cook until warm. Pour broth mixture over drained pasta. Stir cottage cheese, dill, and salt into pasta. Top each serving with freshly ground black pepper to taste and 1 tsp. oil. Serve with lemon wedges.
Note: Nutritional analysis is per 1 1/2-cup serving.