To make the buns, in a bowl, add the warm milk and 1 tablespoon of the brown sugar. Sprinkle over the yeast and let it bloom until a cap of foam forms on the top, 5 to 10 minutes.

In a large mixing bowl or stand mixer with a dough hook attachment, combine the flours and salt. Then add the bloomed yeast mixture, the remaining 3 tablespoons of brown sugar and the thickened flax egg. Knead the ingredients until a dough is formed, about 2 minutes in a stand mixer. Once the dough has formed, add ¼ cup of the butter and continue to knead until the butter is completely worked in adn the dough is smooth and tacky. Transfer it to a clean, oiled bowl, cover it with plastic wrap and leave it in a warm dry place until it is doubled in sized, about 1 ½ hours.

Lightly flour a work surface and a rolling pin and have an oiled muffin tin nearby. Inwrap the risen dough, punch it down in the center to release the air and roll it out to an 11 x 22-inch rectangle. Spread the strawberry jam and the remaining ¼ cup of softened butter all over the surface, and then sprinkle over the granulated sugar, lemon zest and lemon juice. Sarting at the wider end of the dough, cut it into 12 equal strips, then roll the strips tightly into buns. Place the buns in the oiled muffin tin, cover again with plastic wrap and let them rest for 20 to 30 more minutes.

Preheat the oven to 375F. Unwrap the buns and bake them in the oven for 18 t0 22 minutes, or until puffed and golden brown on top. Remove the buns from the oven and make the glaze.

To make the glaze, in a blender, blend the strawberries, lemon juice, lemon zest and confectioners sugar until smooth. Strain to remove the seeds, if you like, and drizzle over the warm buns. Serve.