Remove the saucepan from the heat and start adding flour to the warm mixture. Add flour in small increments (I used 1/4 cup) and mix until incorporated. This is the most critical part of the biscuit dough making. The idea is to obtain a soft and workable dough. If too much flour is added, the dough becomes unworkable once it cools off.
I know at this point it sounds intimidating but it is actually quite easy. Just keep adding flour until the dough is neither soupy nor sticky. I used a hand mixer and added flour until the mixer had difficulty working. At that point I transferred the dough quickly to the counter and worked it out, adding flour by hand. The dough is finished once it is compact enough that it can be rolled out. The dough will be smooth, soft, not sticky and very warm.
I used about 2 cups of flour to obtain a satisfactory dough consistency. In your case, that might vary depending on the size of the eggs you used, how thick your egg mixture was at the end of the heating stage, and on the type of flour used.