A Doughnut Cutter is a special hand-held and operated cutting tool that cuts out a circle, and then a small circle at the centre of that circle.
To use, you you roll out the doughnut dough first, then press the cutter into the dough, and twist the cutter to cut out the shape.
You can get doughnut cutters that will make heart-shaped holes.
Commercially, machines push doughnut batter out in rings of batter straight into the hot oil.
Most recipes will advise to flour the cutter between each cut.
One large biscuit cutter (or glass) to cut out the doughnut plus one small biscuit cutter (or glass) to cut out the centre.
Most sources report that doughnut cutters were invented by a John F. Blondell of Thomaston, Maine in 1872. In fact, he received American patent 128,783 (on 9 July 1872) for an “Improvement in Doughnut Cutters”:
Improvement in Doughnut Cutters
© US Patent Office
“My invention has for its object to furnish an improved device for removing the dough from the cutter-tube automatically… A represents the cutter for cutting dougnuts and other cakes.
B is a tube which serves as a handle in using the cutter, and which passes through and is secured to the center of the top of said cutter, and which is designed to cut a hole through the center of the doughnut or cake. In the middle part of the tube B is placed a coiled spring, C, to the outer end of which is attached a plunger, D.
By this construction, when the cutter is forced through the dough, the follower D is forced inward, compressing the spring C. As the cutter is raised from the dough, the spring C pushes the dough out of the center tube B, leaving said center tube free for making another cut….”
The drawing appears to depict the device made of wood.
His patent, however, makes no mention of restricting the construction to any particular medium.