Cook Burger on Stove - Turns Gray So I've been wondering why whenever I cook burgers, they end up turning into a gray color, and a greasy mess. I'm restricted only to a stove top pan and oven, and I'm sure that's contributing to it, but I'm not sure what to change.

My first guess was that it wasn't high enough heat, but I've waited to heat them up pretty well, and it hasn't really impacted anything. Is it the mix I use to make the burgers? I usually take ground beef, mix it with an egg and breadcrumbs and spices, and then cook some immediately and freeze the rest.

I'm just curious of anything I can do to change the color they come out as, and hopefully improve the taste as much as possible.
If you add egg and breadcrumbs, you aren't cooking a burger, you're cooking meatloaf. 

Try using just good beef with plenty of fat (80% meat, 20% fat is the ideal ratio, lean mince is not good for burgers), and pepper. Get the pan good and hot, salt the burgers well (don't add salt beforehand), brush the burgers with oil, then whack them on the pan, 5-6 minutes a side (depends on thickness) and you'll get a nice brown crust.

A couple of other tips: make the burgers plenty ahead of time so they can sit in the fridge for a good few hours. And never press the burger down with your spatula, you just end up losing all the juiciness. 

Check out The Burger Lab's Top Ten Tips for a Better Burger for more tips.