In a large bowl, mix together the butter, oil, granulated sugar, eggs, and vanilla, until light and creamy.
Pour the batter into the greased muffin tin. Sprinkle the turbinado sugar on top (if using). Bake at 375 degrees F for 18 to 21 minutes.
Nutrition analysis (approximate per muffin): 338 calories, 16.5 g fat, 6.5 g saturated fat, 250 mg sodium, 43 g carbohydrate, 2.5 g fiber, 22.5 g sugar, 4.5 g protein, Vitamin D: 2%, Calcium: 6%, Iron: 16%, Potassium: 3%