Preheat oven to 375ºF. Prepare 18 of the cups in two standard muffin tins by greasing or lining with paper muffin liners.
In a large bowl, thoroughly whisk together flour, sugar, baking soda, baking powder and salt.
In a separate bowl, whisk together the orange juice, pumpkin, butter, oil, vanilla and eggs. Add this to the flour mixture, then fold the ingredients together with a rubber spatula, working gently and stopping when batter is just combined.
Lightly spoon the batter into prepared muffin cups. Top each with a quarter slice of orange, if desired. Bake for 18-22 minutes, rotating pans once halfway through. Muffins are done when tops are golden and spring back when lightly pressed in the centres (or a toothpick tester comes out with just a few moist crumbs). Transfer to wire racks to cool.