Heat butter and oil in a skillet over medium-low heat. Add onions and paprika; cook until onions are soft, about 15 minutes.
Carefully remove husks from corn without tearing; set aside. Cut off kernels, scraping milk from cobs; reserve cobs. Place corn in a food processor or blender; purée until thick. Add corn purée to onions and cook, stirring occasionally, over medium-low heat until mixture is dry, about 15 minutes. Stir in basil and season with salt and pepper. Mix masa harina with 1⁄2 cup of boiling water in a bowl; immediately stir into corn mixture.
To assemble, spoon 2 tbsp. corn mixture into the center of 1 husk (a tender inner leaf works best). Fold bottom edge over filling, fold in the sides, then fold over the top edge to make a neat package. Tie with a strip of corn husk. Repeat process to use up all filling.
Place a few reserved cobs on the bottom of a large saucepan. Add enough water to cover. Line pan with a few remaining husks (the tougher outer leaves), add humitas, then lay additional husks on top. Cover pan and steam over medium heat, adding water if necessary, for 1–1 1⁄2 hours. To check for doneness, unwrap 1 humita: Husk should easily pull away from filling. Cool for 10 minutes. Serve with a sprinkling of sugar and pepper sauce.