Divide the dough into 10 equal portions and form a small ball for each part.
Place each ball on top of a baking tray lined with baking paper, keeping some distance in between.
Brush the buns with olive oil.
Cover with a clean kitchen towel and set aside for about an hour or until they become puffy.
Once the Italian Easter buns are almost ready, prepare the syrup by combining four tablespoons of sugar with a quarter cup of water in a small saucepan.
Place the saucepan over medium-low heat to heat it; mix until the sugar completely dissolves, then set aside.
Preheat oven to 180°C (350°F).
Uncover the rosemary and raisin buns and use a sharp knife to cut two lines crosswise and two lines lengthwise on top.
Brush each bun with the beaten egg.
Place the buns in the oven for 25 to 30 minutes or until they turn darker in color.
Take the tray of pan di ramerino out of the oven and brush with syrup from earlier.
Let cool for about 15 minutes, then serve.