Put the flours, yeast and salt in a large bowl (or stand mixer bowl). Make a well in the center and pour in the water. Mix everything together well (by hand with a wooden spoon or, if by machine, with a dough hook on medium speed) to make a smooth, soft dough ball, 2 to 4 minutes. If doing by machine, continue to knead on medium-high speed for 5 minutes. Otherwise, put the dough on a clean work surface sprinkled with a little flour and knead for about 10 minutes.
To test to see if the dough has been kneaded enough, form into a ball with a nice taut top. Put some flour on your finger and then prod the dough to make a small indent. If the dent springs back all the way, this means the dough is kneaded enough. If not, then knead a little bit more.
Put the dough on the work surface (sprinkled with a little flour if you haven't already done so) and then flatten it out with a rolling pin to about an 8-inch round, 3/4 to 1 inch thick. Put the green onions and thyme in a pile in the center and then bring the sides of the dough up over the filling to enclose. Flip it over so the seam side is down and roll it out to the same size again. Once again, gather the edges up and over, but then knead the dough by hand to incorporate the filling ingredients evenly throughout. You may need to dust with a little more flour as you go if the green onions make things a little damp.
Divide the dough into 10 equal-size pieces and knead each one into a ball with a nice taut top. Put the rolls, seam-side down and spaced apart, on a large nonstick baking sheet. Spray the rolls with a light spritz of cooking spray and then cover with plastic wrap so that it is airtight, but not too tight as the bread needs to grow.
Preheat the oven to 400 degrees F and leave the bread on a chair about 3 feet away from the oven for 45 minutes, or until the bread has almost doubled in size. To test that the rolls are ready, remove the plastic wrap, put some flour on your finger and prod the side of the dough to make a small dent. The dent should spring back about halfway. When it does, it is ready. If necessary, leave it to rise a bit longer.
Once ready, brush the dough balls with the beaten egg and lay 3 sage leaves in whatever decorative fashion you like on top of each one. Bake for 20 minutes, or until the rolls are golden brown and sound hollow when tapped underneath. Once ready, remove from the oven and serve warm.