Grate the carrots. Set aside.
Beat the eggs.
Melt the butter. Add the butter, vanilla and egg to the milk. Set aside.
In a deep bowl, sift the flour. Add the yeast, sugar and salt. Mix well.
Add the grated carrots to the flour and mix well.
Add the liquid to the dry ingredients. Adjust the liquid (milk) as necessary.
Dust with a little flour, knead until smooth and elastic (this might take about 10 minutes).
Leave to rest until it doubles in size. Punch down and then roll out.
Place in a prepared pan, cover with a towel and allow to rise for another 10 to 15 minutes.
Preheat the oven to 375 degrees F (190 degrees C).
Bake until golden brown, or for 20 to 25 minutes.
Remove from the pan and cool on a rack before slicing.