One handed kneading is a well known method for making bread dough. For example, in her book Breads from the La Brea Bakery, Nancy Silverton described the process as follows (at page 44):
Here's what you do. Remove the dough from the bowl, if you're using one, and place it on a sturdy work surface. With one continuous motion, grab the end of the dough closest to you, fold it toward the other end, gather one end in your fist, lift and flip the dough in midair, then whack it down hard on the work surface. Immediately grab the dough again and repeat the motion over and over for about 5 to 7 minutes. As you work, the dough will become less sticky, more elastic, and more difficult to manipulate. Slowly, it will start to take on the rough shape of a rounded loaf, or boule.
Ms. Silverton felt it was "nice to have one clean hand with which to answer the phone, burp the baby, or pat the dog."
I tried Ms. Silverton's one-handed kneading method when I made some of her sourdough breads. I later learned that the method was used to make French breads where the workers were required to do a hundred or more repetitions of the one-handed slam and they dared not stop until they got to the desired number.