Welcome! I believe I understand your question. Please see above link.
The idea here is to think about the mirror modifier. As such, I started with a plane situated in the upper right quadrant (in Top View).
Then, add some extra geometry to your plane (it helps with the hole that's coming).
Pick a vertex and snap your 3D cursor there, so you can add a Circle.
Select the circle, then the plane, then go into Edit Mode. Pick Knife Project to cut a hole on the plane. The Circle can now be deleted.
Deleting the faces inside the circle leaves you with a hole! Extrude the plane a bit, then select the edges of the hole and Ctrl-B to bevel it.
Now for the Mirror Modifier. The key to understanding this modifier is that it mirrors around the Origin. That's why you see me placing the 3D cursor and changing the object's Origin- I'm controlling where the mirroring happens.