Khachapuri, aka Georgian cheesy bread

Khachapuri is delicious.  It's the number one food I miss from Russia, though it's not Russian.  To catch up - I spent seven months teaching English in Russia after I graduated college.  I lived in the outskirts of Moscow at Domodyedovskaya - near the airport.  Everyday on my way to the metro I would pass by a bakery that always had a line around the block.  People would buy different kinds of fresh baked Georgian bread for really cheap.  There were no baguettes here.  My favorite item was the khachapuri, the cheesy bread..  My roommate and I became regulars at this bakery and soon they referred to me as "San Francisco" instead of my name.  They liked me so much I even got preferential treatment some days, allowing me to come to the back door and skip the line to get my fresh khachapuri.  I even inadertenly went on a date with their son who speaks no English (nor I Russian really).  He followed me from the shop talking in Russian as I talked back in English and we played shuffle ball at the mall and went to the bookstore. Before I left the family offered me their son's hand in marriage (joking...I think), and while I was set on going back to the states, I did contemplate the perks of marrying into the Georgian bakery (khachapuri for life!).  With all this said, I have been waiting oh so patiently for an opportunity to make my own khachapuri to try and replicate what I lost.  What I have isn't perfect (it didn't even come out even - though I have faith in this recipe).  However, it's pretty good, and it definitely shares some key similarities.  I plan to make this often in the future and tweak it accordingly until it lives up to my memory.  This recipe was taken from Gourmet magazine.

2 1/4 tsp active dry yeast
7 TB warm water
1 2/3 cups AP flour
3/4 tsp salt
1 egg, lightly beaten
1/2 lb Harvati cheese, or a substitute to your liking, grated
1 tsp butter, melted

• Mix yeast with warm water, stir in 1 TB of flour.  Let stand until creamy and yeast activates (about 5 min).  Make sure yeast activates (if not, start over!).
• Mix salt and flour, stir in egg and then yeast mixture, form dough.
• Knead dough on a floured surface until it comes together and becomes smooth and elastic (about 5-7 minutes).  It will start out feeling very hard.  You're close to being done with kneading when the dough becomes softer and very smooth.  If you're not sure how to knead dough, look here.  Form a ball of dough and let it rest in a container covered with plastic wrap, pushing it down every hour for 3 hours.
• Preheat oven to 500F, put bread/pizza stone in oven for baking (or sheet pan you plan to use)
• Grate cheese, form it into a ball.  Flatten dough out into a 7in circle, put cheese in the center and gather the edges around the cheese.  Fasten the dough at the top and push down, pressing out the cheese from the center to distribute it evenly among the bread.  Flatten into an 11in circle.
• Score the top to expose the cheese a little.  Bake on the stone for 10-12 minutes, brush with melted butter, and then continue for 3-5 minutes.
• Serve hot!

Normally khachapuri is flat.  Make sure you spread the cheese evenly on the inside.  I had a section without cheese (just bread) and it rose higher, making the bread lopsided.  Lesson learned.  Does not affect delicious factor.