Begin by warming your milk and add to the mixing bowl. Add in your dry yeast packet and sugar and let sit about 10 minutes. You will know the yeast is working if the mixture begins to form bubbles on top.
While waiting to see if the yeast is active, peel and grate your carrots and set aside.
Next, add the melted vegan butter, grated carrots, and vanilla to the mixing bowl and stir to combine. Then, add the flour and salt to the mixing bowl ½ cup at a time and mix. Once a dough forms, switch a standing mixer to the bread hook and knead for 5 minutes. If kneading by hand, remove the dough and knead on a well-floured surface for 5-10 minutes until an elastic dough forms.
Lightly spray a large bowl with oil, form the dough into a ball, and add the dough to the bowl. Oil the top of the dough so it does not dry out. Then, cover the bowl and let the dough rise 1-1.5 hours until it has doubled in size. You will know the dough is done by pushing your finger into the dough and the dough will not spring back.