Heat the milk, in the microwave or a saucepan, until it is “fingervarm” (finger warm), meaning it should feel warm to the touch but not hot. Add your yeast and sugar, stir, and leave it for 5-10 minutes until the mixture starts to bubble up, meaning your yeast is alive and not expired.
While the yeast is sitting, peel and grate the carrot.
Add the egg yolk, grated carrot, sunflower seeds, and salt to a large bowl or the bowl of a stand mixer and mix well. Once the yeast mixture has bubbled up a bit, add it to the egg mixture. Mix well.
Slowly add the flour and softened butter, mixing with a wooden spoon or the dough hook of the stand mixer until the dough starts to come together. Reserve a small amount of flour. If the dough is sticking to the sides of the bowl or your hands, add the remaining flour and if needed, a few more tablespoons at a time. If the dough is remaining dry and crumbly, add a little bit more water.
Knead until smooth and elastic, about 10 minutes, either by hand or using the dough hook on the stand mixer. Continue to add a bit more flour if the dough is too sticky; it should be soft and smooth, not too sticky nor too dry.
Cover the dough with cling film or a clean dishtowel and place in the fridge overnight for 8 hours, or let rise at room temperature (if room temp is very cold wherever you are, put it in a warm place, i.e. under a light) for about 1 hour or until doubled in size.
Once your dough has doubled in size, prepare a loaf pan (we used a medium sized loaf pan) by buttering or oiling the sides of the pan and cutting a piece of parchment paper to lay across the pan for easy removal.
To shape the loaf, dump the dough out on a clean surface. Using your hands, stretch it out into a rough rectangle shape, with a width equivalent to the size of your loaf pan.
Start rolling from one end, keeping the roll very tight.
Once you have rolled it up, pinch together any creases and roll the loaf against the countertop lightly to create surface tension and help close the crease on the bottom of the loaf and also along the edges.
Place the loaf in the loaf pan.
Let it rise for another 30 mins to an hour, until doubled in size. This timing will very much depend on the temperature of your house. While it is rising, preheat the oven to 350 F (175 C).
Once the loaf is ready, brush with egg wash.
Bake for about 30 minutes until golden brown and the bread sounds hollow when you tap it.
Remove from the loaf pan and let it cool for at least 20 minutes before slicing and enjoy!