Place the yeast, sugar and milk in the bowl of a stand mixer. Set aside for 5 minutes until slightly frothy.
Add the egg yolks, melted butter, flour and salt. Fit the stand mixer with the dough hook and mix everything together on a medium speed for 6 minutes until soft, elastic and slightly sticky. Pour a bit of vegetable oil over the dough in the bowl, then turn the dough in the bowl to coat.
Cover with a damp, clean kitchen towel and leave somewhere warm until doubled in volume (1-2 hours).
Shape the buns:
Use some of the melted butter (from the filling ingredients) to brush the inside of a 9 x 13-inch rectangular pan.
Tip the risen dough out onto a lightly floured work surface. Divide into 4 equal pieces.
Roll two of the pieces out into 8 x 10 inch rectangles. Brush a quarter of the melted butter over each rectangle. Sprinkle on 1 tablespoon of the sugar. Lay 1/2 cup of the sliced strawberries over each of the rectangles. Starting at the long edge, roll up into logs. Cut each log into five 2-inch pieces. Have the buttered 9 x 13 inch pan with the long edge facing you. Place the cut pieces along the bottom long edge of the buttered 9 x 13 inch pan, in rows of 5.
Roll another of the dough pieces out into an 8 x 12 inch rectangle. Brush a quarter of the melted butter over the rectangle. Sprinkle with 1 tablespoon of the sugar and lay on the remaining strawberries. Starting at the long edge, roll up into a log. Cut into six 2-inch pieces. Place in a 3 x 2 grid on the top right-hand side of the buttered pan.
Roll the last dough piece out into an 8 x 8 inch square. Brush with the remaining butter and sprinkle 1 tablespoon of sugar over it. Scatter over the blueberries, roll up into a log and cut into four 2-inch pieces. Place in a 2 x 2 grid in the top left-hand side of the buttered pan.
Cover the pan with a damp, clean kitchen towel and leave somewhere warm for 30 minutes to rise.
Meanwhile, preheat the oven to 350 degrees F.
Once the buns have risen and the oven is preheated, remove the kitchen towel and bake the buns for 20-25 minutes until well risen and golden on top.
Let cool completely before piping horizontal stripes along the rows to make the white stripes of the ‘flag’ and dots over the blueberry buns to represent the stars.