It's mainly two issues. One is you need to whisk the eggs in really well so the batter doesn't separate as it bakes, and another is that your butter is too hot. When you melt butter all the way, it separates into pure butterfat and milk solids. This separated butter can make a runny layer in your chess pie. What you want to do is melt the butter without breaking the emulsion, and that means making sure it stays creamy and opaque but very very soft so it's easily whisked into the rest of the batter.