Honestly, it looks like it's just too high a percentage of egg... and maybe not enough cheese. I don't know that it can't work with that much egg but most of the recipes I've found just now use much more dairy to egg and have other ingredients to make them creamy.
For comparison purposes, you're using less than a quarter cup of liquid to two eggs or 1.5 tbsp/egg.
For example, this one on Food & Wine, uses 3 eggs and 1 cup half and half. It also has a cup of cheese and lots of other ingredients. The egg is clearly just a binder to hold things together. So, that's over 5 tbsp half and half per egg.
This one on allrecipes has 4 eggs and 1-1/2 cups of milk... and lots of cheese. That's 6 tbsp milk per egg.
This one from food.com is closer to yours in ratio, with 5 eggs and only 3/4 cup milk but that's still over a quarter cup more liquid (12 tbsp instead of 7.5 tbsp per five eggs)... and it has you add two cups of other stuff, first suggestion being cheese.
I've found other recipes that use 6 eggs to 3/4 cup cream, too... which, again, is closer but still about 1/4 cup short.
I recommend adding more wet to your mixture to cut the egg.
Also, if you were baking at the traditional 350 F (175 C), you might lower your temperature a bit. Smaller things often do better with a slightly lower oven. This gives you more room for error. I bake mini-cupcakes at 325 F instead of 350 F for this very reason.
So, try raising your cream to 4-5 tbsp (or maybe try a more watery dairy like half and half), add some cheese (cheese is creamy, remember?), lower the temp to 325 F (160 C) and try again.
Sorry, that's a lot of different things to try... but since I don't know your oven temperature, that part is more of a guess.