Cutting small felt circles – am I missing the obvious? Sewing Machines Parts and Sales in Los Angeles

I need/use about 120 felt circles every month as eyes for the dolls I make. They need to be 3/8" ish (no bigger than 1/2"). Cutting by hand is a no go. Right now, I'm ordering from an Etsy vendor but it would be so much handier just to crank out circles here on my own.

But I can't seem to find any practical options. There seem to be a couple of different kinds of dye cutting machines at $200+ and that's all I can find. I did try a paper cutter. It just couldn't handle even the thinnest felt.

Is my best bet buying them on Etsy? Or is there a trick I haven't found yet?