Roast the peppers: Preheat oven to 450°F. Place pepper halves skin-side up on a baking sheet, drizzle lightly with olive oil, and roast for 20–25 minutes until skins are blistered and blackened in spots. Transfer to a bowl, cover tightly with plastic wrap, and let steam for 10 minutes (this loosens the skins). Peel away the charred skin and remove any remaining seeds.
Prepare the chickpeas: Pat chickpeas dry with a paper towel — this helps them blend more smoothly.
Blend until silky: In a food processor, combine tahini, garlic, lemon juice, olive oil, and cumin. Process for 1 minute to let flavors meld. Add chickpeas and processed peppers; pulse several times before blending continuously for 2 minutes until very smooth. Scrape down sides as needed.
Adjust consistency: With the processor running, slowly add water one tablespoon at a time until hummus reaches your preferred thickness (usually about 1/4 cup). Season with salt to taste — start with 3/4 tsp and adjust after tasting.
Serve or store: Transfer to a bowl, drizzle with olive oil if serving immediately. Store in an airtight container in the refrigerator for up to 5 days. Let come to room temperature before serving for best texture.