Make the buns: In a medium bowl, whisk together ⅓ cup lukewarm water, the honey, and yeast, and set aside until the mixture is foamy, about 10 minutes. Stir in ½ cup of the all-purpose flour, cover with a clean kitchen towel or plastic wrap, and set aside in a warm place until the mixture is bubbly and starts to rise, about 20 minutes.
To the bowl of a stand mixer fitted with the paddle attachment, add the remaining all-purpose flour, the bread flour, sugar, and salt. Mix on low speed until combined, then add the eggs, lemon or orange zest, and the reserved yeast mixture, and continue mixing until smooth and combined. Using a plastic bowl scraper or silicone spatula, scrape down the bottom and sides of the bowl and the paddle attachment. Turn the mixer up to medium-low speed, then add half of the butter, and mix, stopping to scrape down the bowl and paddle occasionally, until the butter is completely incorporated into the dough. Add the remaining butter and continue mixing and scraping until completely incorporated, then, with the mixer still running, slowly drizzle in the olive oil. Turn the mixer up to medium speed and continue mixing until the dough is very smooth, elastic, and slightly sticky, 8–10 minutes.
Lightly oil a large bowl, transfer the dough into it, then cover with the kitchen towel or plastic wrap. Set aside to rise in a warm place until doubled in size, 1–1½ hours.
Line two large rimmed baking sheets with parchment paper and set aside. Turn the dough out onto a clean work surface. Using a large chef’s knife or bench knife, divide the dough into 10 equal pieces (about 70–75 grams each). Round each piece into a smooth balI by using the palm of your hand to roll it against the work surface in a circular motion, then, working with one ball at a time, use both hands to roll each piece back and forth against the work surface while using the outsides of your hands to put gentle pressure on two sides of the ball, creating a tapered oval shape, about 5 inches long. Transfer the buns to the lined baking sheets, leaving at least 2 inches between each bun. Cover each pan with a clean towel or plastic wrap and let rise in a warm place until the buns are puffed, very soft, and not quite doubled in size, 30–45 minutes.
Meanwhile, preheat the oven (with one of its racks positioned in the center) to 350ºF. Working with one tray at a time, bake the buns, rotating the tray halfway through cooking, until golden brown, 15–17 minutes.
While the buns are baking, make the syrup: In a small pot over medium heat, combine the sugar and 3 tablespoons water. Cook, stirring frequently, just until the sugar is dissolved, about 2 minutes, then remove from heat and set aside.
As soon as the buns come out of the oven, brush them generously with the syrup, then cool completely.
Using a serrated knife, split the buns vertically down the center without cutting all the way through, leaving the two halves connected (like hot dog buns); fill with sweetened whipped cream and serve immediately.