Preheat the oven to 350°F and line 12 to 14 muffin cups.
Whisk the flour, baking powder, baking soda, salt, cinnamon, granulated sugar, and brown sugar together in a large bowl and set aside.
Whisk the cooled melted butter, eggs, and vanilla in a separate bowl, then stir into the dry ingredients until just combined. Gently fold in the shredded carrots and mashed banana until fully incorporated, taking care not to overmix.
Fill the muffin cups three-quarters full with batter and top each with 1 ½ teaspoons of pecan chips. Bake for 17 to 20 minutes until the muffins spring back when touched or a toothpick comes out clean.
Cool the muffins in the pan for 2 to 3 minutes before transferring to a wire rack. Serve warm, and store completely cooled leftovers in an airtight container at room temperature for up to 2 days or in the refrigerator.