How to avoid burned layer on seared hamburger?

I usually make my hamburgers at home by putting a little oil in a pan and then just placing the patty in it on medium heat for 10-15 minutes.

Inevitably, while the meat ends up about medium rare, there's a semi-burned layer along the bottom, where it's browned and crusty. I always have to pick this off and I'm finally sick of it.

What am I doing wrong?