Preheat oven to 375 degrees F. Line two baking sheets with parchment paper or nonstick foil.In a small bowl, combine the bran cereal and water. Set aside and allow bran to soften.In a large mixing bowl using an electric mixer, beat the butter, oil and both sugars until creamy. Beat in the eggs, one at a time, then beat in the vanilla.Stir the softened bran into the batter.
Combine the flour, baking soda and salt, and gradually add the flour mixture to the batter, stirring by hand or using lowest speed of mixer.Stir in the chocolate chips and nuts.Using a level tablespoon, shape dough into balls and arrange about 2 1/2 inches apart on baking sheets.
Bake cookies for 10 to 13 minutes on center rack (they should be golden brown and appear set).
Remove from oven and let cool on baking sheet for 10 minutes.