Combine sugar and warm water in the bowl of a stand mixer and stir. Top with the yeast and let stand until bubbling, about ten minutes.
Add butter and mix on low speed with the dough hook. One cup of flour at a time, adding and mixing until all the flour is included and a moist, sticky dough forms.
Transfer dough to a clean surface that has been lightly floured. The dough has a hint of stickiness. Work into a ball after a few kneadings.
Place the ball into a big bowl that has been oiled (we like to use our misto for this) and then cover it with plastic wrap. Allow to rise until doubled, about 1 hour.
In the meantime, combine all of the pesto's components in a food processor or blender. Until creamy, blend. If a looser consistency is what you're after, add one tablespoon of water.
If you're not shaping it into a tree or wreath, grease a big baking pan or a 9 x 13 baking dish. Put away.
Cut the dough into 21 equal-sized pieces, each weighing between 1.2 and 1.4 ounces, using a kitchen scale. Use this to form the shape of a tree or wreath; refer to the recipe notes if baking in a baking dish.
Using your palm, carefully spread each piece of dough open. Using your free hand, remove a little amount of cheese and place it in the middle of the dough. Pinch the dough closed by gently folding the edges up around the cheese. Place in pan or dish with seam side down, leaving about 1/2 inch between each to allow for rising. Continue with every dough ball. (For reference, view the photographs in the post.)
After gently covering with a fresh kitchen towel or linen, allow it to rise for an additional thirty minutes.
Set the oven's temperature to 350.
Sprinkle some mozzarella cheese into the dough ball corners once they have risen once more. Apply a thick layer of pesto to the tops of the rolls and the corners using a silicone brush. Feel free to use as much pesto as you like—a minimum of 1/2 cup and a maximum of 1 cup.
Add the last of the mozzarella cheese to finish.
Bake the cheese for 20 minutes, or until it is browned and melted.
Present and savor!