Preheat the oven to 425°F.
Line two muffin tins with muffin liners and set aside.
Shred the apple and carrot, then gently pat dry with a paper towel to remove excess moisture.
Add the shredded apple and carrot to the fermented dough.
In a separate bowl, whisk together the melted butter, honey, eggs, Greek yogurt, vanilla extract, and cinnamon.
Pour the wet ingredients into the fermented dough.
Using an electric hand mixer or stand mixer, mix until fully combined. The batter will be thick at first but will come together smoothly.
Mix in the baking powder, baking soda, and salt until just incorporated.
Divide the batter evenly among the prepared muffin liners.
Bake at 425°F for 10 minutes, then—without opening the oven door—reduce the oven temperature to 350°F.
Continue baking for an additional 10 minutes, or until the muffins are set and a toothpick inserted into the center comes out clean.
Remove from the oven and allow to cool slightly before serving.