In large pot over medium heat, or microwave-safe bowl, add oil (or butter), water and milk. Heat to 110-115°F. Pour into a mixing bowl.
Add sugar and egg; stir in yeast. Whisk until mixture is smooth.
Add flour, cornmeal, onion, salt and seasoning. Stir with heavy wooden spoon. If necessary, work in a little additional flour with your hands until the dough is no longer sticky. Knead on floured surface for 2 to 3 minutes. Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until indentation remains after poking dough with finger down to second knuckle, about 1 hour..
Punch down, cover and let rest 10 minutes. Turn out onto a lightly floured surface. Divide into 24 equal pieces (cut dough into 4 pieces, the cut each of those into 6 pieces). To shape, roll each piece into a 6-inch long rope. Tie in loose knot and tuck ends under. Place rolls onto greased 9x13-inch pan. Cover and let rise until indentation remains after lightly touching.
Preheat oven to 375°F. Brush tops with 2 tablespoons melted butter or oil. Bake 15 to 20 minutes or until golden brown. Cool on wire rack.