Toast cumin in a small frying pan over medium-high heat, stirring often, until fragrant, about 2 minutes. Pour from pan into a large bowl. Stir in oil, lemon zest and juice, garlic, salt, and black pepper.
Seed peppers and cut into 1- to 1 1/2-in. pieces. Slice cucumber into 1/4-in. rounds and cut in half again if large. Add peppers, cucumber, and chickpeas to salad dressing and toss to blend well. Let stand about 1 hour, then stir in parsley.
Make ahead: Up to 4 hours, chilled airtight; add parsley just before serving.