Heat the water to between 105°F and 115°F. Add a pinch of sugar and the yeast. Stir briefly and then set aside for the yeast to activate. When the yeast is bubbly and risen, after about 5 minutes, proceed with the recipe.
In the bowl of a stand mixer fitted with a dough hook, combine the warm milk, sugar, 1 beaten egg, and 1 tbsp melted butter with the yeast mixture. Stir together. Add the flour and ½ tsp kosher salt to the mixer.
Mix, using the dough hook, until the dough starts to come together. Scrape down the sides occasionally to encourage the dough to come together. If the dough is too sticky and sticks to the side without forming a ball, then add more flour, a tablespoon at a time.
Continue mixing with a dough hook on low speed for about 5 minutes until the dough is soft and stretchy. After mixing, take the dough out and lightly knead a couple of times on the counter to bring it together into a smooth ball.
Transfer the dough to a greased bowl. Rub a little oil on top of the dough. Cover with cling film or a tea towel and then set in a warm place to rise for 1 to 1 1/2 hours until double in size.
In a food processor, combine the baby arugula, fresh basil, half the minced garlic, lemon zest, remaining ½ tsp kosher salt and pepper. Pulse until the greens are very finely chopped. Add the boursin cheese and pulse just until the mixture is combined and smooth. Transfer to a bowl and chill until ready to assemble.
After the dough has risen, punch it down to deflate completely. Transfer the dough to a lightly floured counter. Divide the dough into thirds. Shape each piece into a ball, setting two aside. Begin to roll one piece out into a 10-inch circle. If the dough feels tight and begins to spring back while rolling, set it aside to rest while starting to roll the other two pieces.
Alternate rolling between the three pieces of dough, until you have three 10-inch circles of dough. Place a sheet of parchment paper on the counter and top with one circle of dough. Spread half of the filling evenly over the dough. Sprinkle evenly with half of the finely grated parmesan cheese. Top with another circle of dough and then repeat with the remaining filling and parmesan cheese. Lastly, top with the remaining circle of dough.
Mark out a 3-inch circle in the middle of the dough with a glass or circle cutter. Use kitchen shears to cut strips into the pastry stopping when you reach the marked centre. Make sixteen strips, cutting it first into quarters and then cutting each quarter into 4 strips.
To shape the star, pick up two strips and twist away from each other two times. Bring the two ends together, pinching to make a point. Repeat with the next two strips, until you have eight twisted points. Slide the parchment paper onto a baking sheet and cover with a tea towel. Let rise in a warm place for 30 minutes or until doubled in size.
While the dough is rising, preheat the oven to 350°F. Prepare an egg wash by beating together the remaining egg and a splash of water. Use a pastry brush to brush the egg wash over each twist.
Bake for 20 to 25 minutes until a golden brown. The bread is done when it sounds hollow when tapped on the bottom.
While the bread is baking, make the garlic butter. Melt the remaining butter in a small saucepan over medium heat. Add the remaining minced garlic and sauté briefly until fragrant. Remove from the heat before the garlic browns. Stir in the chopped parsley.
Brush the garlic butter evenly over the star bread after it comes out of the oven. Brushing with the garlic butter while the bread is still warm will allow it to absorb the butter more easily. This bread is delightful served warm. Enjoy!