Make the buns by whisking 1/3 cup of lukewarm milk, yeast and honey in a large bowl. Let the mixture stand for 10 minutes before adding the rest of the ingredients. Mix in 1/2 cup all-purpose flour. Cover the bowl with plastic wrap or a kitchen towel and let the mixture rise for 20 minutes. Add the all-purpose flour, bread flour, sugar, salt, and remaining flour to the bowl of a stand mixer equipped with the paddle attachment. Mix the ingredients on low speed until well combined. Next, add the eggs, orange zest and the saved yeast mixture and mix until smooth. Use a silicone spatula to scrape the sides and bottom of the bowl. Mix in one-half of the butter at a time in the mixer on low speed until it is well incorporated. Continue to mix and scrape the butter until it is fully incorporated and adding the rest of the butter. Then, while the mixer is still running, drizzle in the olive oil. At this stage mix on medium speed until dough becomes smooth, a bit sticky and elastic. This should take a maximum of 10 minutes. Add a small amount of oil to a large bowl. Move the dough to it and cover it with plastic wrap or a kitchen towel. Allow to rise for 1-1/2 hours at room temperature, it should double in size. Place parchment paper on two large, rimmed baking sheets and place them aside. Place the dough on a work surface. Divide the dough into 10 same-size portions using a large chefs or regular kitchen knife. Each piece should be rolled into a ball using your palm. Next, roll the dough against a work surface using your hands. Use your hands to gently press down on the two sides of each ball and create oval tapered shapes (5-inches long). Place the buns on the baking sheets. Make sure there is at least 2 inches between each one (this will give them room to rise). Place the buns on the lined baking sheets and cover them with a towel or plastic wrap. Let rise in warm until they are puffy, soft and have not doubled in size. This can take about 40 minutes. Place the buns on the lined baking sheets and cover them with a towel or plastic wrap. Let rise in warm until they are puffy, soft and have not doubled in size. This can take about 40 minutes. Preheat the oven to 350F with one of the racks in the middle. Bake the buns and rotate the tray halfway through baking to ensure that the buns are golden brown. This takes between 15-18 minutes. Make the syrup while the Maritozzi buns bake. Over medium heat, using a small pot, combine the sugar with 3-4 TBSP of water. Stirring frequently, cook the syrup for 2 minutes. Then, remove from heat and let cool. After the Maritozzi buns have been removed from the oven, brush them with the syrup (Be generous) and let them cool completely. Use a small knife to cut the buns vertically along the middle and split them, but not all the way. Fill the buns with whipped cream and serve right away.