Step 1: Char the peppers on all sides. You can do this “caveman” style (laying them directly on the burning embers of a charcoal grill), by direct grilling on a gas grill, or even by charring them on your stovetop burners. The idea is to blacken the skins on all sides (this will take about 3 minutes per side). The charring imparts an incredible smoke flavor. Transfer the peppers to a plate to cool, then scrape off the burnt skin with a paring. (Don’t worry about removing every last bit—a few pieces of black help add color and flavor.) Cut the peppers into 1-inch pieces, discarding the core and seeds.
Step 2: Place the peppers, chickpeas, feta, and garlic in a food processor and puree to a smooth paste. With the processor running add the olive oil, lemon juice, hot pepper flakes, and salt and pepper to taste: the mixture should be assertively seasoned. Transfer the dip to a shallow bowl and serve with grilled or fresh pita bread for dipping.