First, make standard challah dough and take a third of that batch for this challah. Divide your dough into 3 equal chunks of dough (or however strands you'd like to braid). I use a kitchen scale, but feel free to eyeball it for a more rustic look.
Take one of the dough chunks and put it onto your worktop. Cover the other two chunks with a kitchen towel so they don't dry out. Roll the dough into a long snake shape and then flatten it into a long rectangle with a rolling pin. Take ¾ cup of cheddar and put half of it onto the top of your flattened dough, and use the rolling pin to roll it into the dough. Flip it over and repeat with the other half of the ¾ cup of cheddar. Arrange scallion pieces onto the dough along the entire length of the rectangle. Fold the long sides in over the scallion and pinch them together to form a long, scallion-stuffed roll of cheesy dough. Repeat with the other two chunks of dough.
Arrange the dough "snakes" next to one another and pinch them together at the top. Braid your challah, pinching again at the bottom and then tucking the end underneath the challah. Flip your challah around so the top is now the bottom and tease the strands away from one another and braid them as well, pinching them at the end and tucking the end under the challah like before.
Cover with a kitchen towel and set aside for an hour to rise. Preheat the oven 350°F. Once your challah has rested, place it onto a baking sheet lined with parchment paper (or an oiled bread tin) and brush the top of it with egg yolk.
Bake at 350°F for about 15 minutes and then remove from the oven and egg yolk wash where the challah expanded and therefore doesn't have any egg wash on it. Return the challah to the oven for 20-25 minutes, or until golden.
Remove from the oven and make sure that the challah is cooked through. You'll know it is when you gently try to tease braids apart (on the end or somewhere else inconspicuous)- there should be no evidence of doughiness, and the braids want to stay intact, almost like there are strands of gluten holding them together. Remove the challah from the tray let cool before slicing.