Bring sweet potatoes and malanga with water to cover and 1 teaspoon salt to a boil in a large Dutch oven over medium-high heat, and cook 20 minutes or just until tender. (Do not cook until mushy.) Drain well. Cool; peel sweet potatoes. Grate malanga and sweet potatoes into a large bowl.
Stir together 1 cup flour, baking soda, and remaining 1 teaspoon salt in a large bowl. Stir in beaten egg yolks; gently stir in grated potatoes and malanga. If desired, stir in anise extract.
Divide dough into 24 equal pieces. With floured hands, roll each piece into a ball; roll each ball into an 8-inch rope on a floured surface, adding additional flour to hands and surface as needed. Shape each rope into a figure eight, pinching ends together.
Pour oil to a depth of 2 inches in a Dutch oven; heat to 375°. Fry buñuelos, in batches, 3 minutes on each side or until golden brown. Drain well on paper towels. Sprinkle with sugar; serve immediately.