My carburetor keeps dumping gas

Look how BIG the epoxied area is compared to the one on the rear. There surely appears to be a hex under "all that". There's certainly "something" under there "besides" epoxy.
That is an old-style non-racing Holley, and they are adjusted internally, like the majority of street carbs.
What's under that epoxy, is the same as what you see on the rear bowl. I wouldn't say that those plugs are prone to leakage, but ..... I've seen a few epoxied up like that.