Heat a medium pot over medium heat 2 minutes. Pour in 1/4 cup oil, wait 1 minute, and then add onion, 3 cloves garlic, chile, thyme, and bay leaf. Cook, stirring, until onion softens, 3 to 4 minutes. Stir in paprika, cinnamon, and cayenne; then stir in chickpeas and 2 tbsp. water. Cook over low heat, covered, stirring occasionally, 10 minutes to blend flavors. Season with salt and let cool. Remove bay leaf.
Whirl chickpea mixture in a food processor with 2 tbsp. more water, salt and pepper to taste, tahini, cumin, remaining garlic, and 2 tbsp. oil. Purée until smooth, 7 to 8 minutes, whirling in up to 2 tbsp. more oil and 1/3 cup water to achieve a smooth, glossy consistency. Serve at room temperature.