Stir cumin in dry skillet over medium heat until lightly toasted, about 2 minutes. Transfer to mortar or spice mill; grind. Heat 1/4 cup oil in large saucepan over medium-high heat. Add garlic and cumin; stir 1 minute. Add chickpeas, 1 teaspoon coarse salt, paprika, and cayenne; saute until chickpeas begin to darken, about 5 minutes. Pour chickpea liquid into 2-cup measuring cup; add enough water (if necessary) to measure 2 cups. Add liquid to chickpea mixture; bring to boil. Reduce heat to medium; simmer until chickpeas begin to soften, stirring often, about 10 minutes. Pour chickpea mixture into strainer set over bowl; reserve cooking liquid. Transfer chickpeas to processor; add 3/4 cup of reserved cooking liquid. Add 1/2 cup oil; puree until smooth. Season with salt and pepper. Cool. Do ahead Can be made 1 day ahead. Cover; chill. Bring to room temperature before using.