Preheat oven to 350°F (177°C). Line a muffin tin with paper liners or grease lightly. In a large bowl, whisk together flour, baking powder, baking soda, cinnamon, and salt until evenly combined.
In another bowl, whisk the eggs, sourdough discard, brown sugar, granulated sugar, melted butter, and vanilla extract until smooth and slightly thickened.
Pour the wet ingredients into the dry and stir gently until just combined, don’t overmix! The batter should look thick but moist.
Fold in the grated carrots and grated apple.
Scoop the batter evenly into 12 muffin cups. Bake for about 18–22 minutes, or until a toothpick inserted in the center comes out clean and the tops are golden brown.
Let muffins cool in the pan for 5 minutes before transferring to a wire rack. Serve warm or at room temperature with butter, honey, or your favorite spread.