I'm new here (this is my first post) so I hope you don't mind me chiming in. I'm not a certified electrician, but I'm a draftsman for an electrical contractor. As with everyone else you really should have a qualified electrician take a look at that box.
First thing the feeder is 10 AWG (orange type NM "Romex" is 10 AWG, and most likely this was installed 2001 or later). If anyone is interested search for "type NM cable color" on Google (or any search engine) for color codes for type NM cable aka "Romex."
I'm not sure what that box is, but it almost looks like a home made contraption. I would have a qualified electrician replace that with something like a
SquareD QO612L100 would work great for that. You could then even reuse that twin breaker (+/- $35). Just because that panel is rated for 100A, doesn't mean you can't feed it with something LESS. We've used that panel full of QOT breakers when we've needed a lot of circuits in a small package.
It appears it's already burnt something once.
I believe the left breaker is a SquareD
QOT2020 (stab on, twin 20A) breaker. These can be used as a 2 pole (240V) breaker with the proper handle tie QOTHT installed. I don't believe that panel can be used as a 240V panel unless you pulled out both of those twin breakers and installed a standard 30A 2 pole breaker (SquareD #QO230).
At the least the grounding needs to be fixed. That single lug should be replaced by a ground bus bar (much like the neutral bus bar on the right side.) That lug is triple lugged. And I think even the wire is under it's min. size. Even that neutral bus bar doesn't look right. If it's screwed to the enclosure directly that's bad. A qualified electrician should look at that panel no mater what.
You may be in luck that the #10 NM cable is in conduit (shouldn't be) and maybe that goes back to the main panel. If that is the case, it should be "fairly easy" to pull out the NM cable and pull in larger building wire. The NM cable exiting the right upper side might also be in conduit, but I can't tell. The bottom exiting NM appears to correctly use a Romex connector. Those could probably both be #14 AWG (or #12.)
Hopefully that's helpful to you. And good luck with the oven build.