I get part drawings weekly with such features, flat bottomed counterbores with no provision for drill bit angles at the bottom of the hole, the cost of doing such a thing should be included in your quote. If a hobby project do as mentioned above, bang a center cutting endmill in there from the tool post or tail stock just short of finished depth then use a boring bar to finish the ID and Z axis depth that you desire.
I ran a 150 part job last year, 1.50" aluminum rounds, flat bottomed counterbore 1.375" Dia. X 1" Depth, I ran a 1 1/4" 2 flute endmill .990" deep at .020 inches per revolution held in a QCTP holder at 750 RPM's, finish boring, parting and OD turning at 1500 RPM's. This lathe has a 2 speed motor and the simple twist of a switch doubles or halves the spindle speed. After several dozen parts I failed to reduce the speed for the endmill operation and banged that tool in there at 1500 RPM's, it worked fine but made a terrible sound. I ran the rest of them that way(-:
Talk about chips, over 75% of the solid bar was reduced to chips, 18" turned into chips by the 1/8" parting tool.
We did a job last Winter, 11000 parts, first step was cut the blanks with a largish bandsaw that uses 1/16" wide blades, .06" X 11000 cuts = 660" or 55 Ft. lost to the saw alone, we are only a small shop I can not possibly imagine what a company capable of making 1,000,000 of these parts would look like.