Country Fried Steak & Gravy

This recipe is from my friend Dawn D. Believe it or not, I've never had country fried steak. (Gasp! I'm from the SOUTH!) I've always wanted to try it, but never had a good recipe. I think this is the one and better yet, she's also included a gravy recipe.

1 cup vegetable oil
1 lb. round steak (I buy the ones already sliced up in the meat section)
salt
black pepper
1 egg beaten
3 cups plus 3 tbsp. milk
1 1/2 cups plus 3 tbsp. all purpose flour

Heat oil in large skillet.
Use meat mallet to pound out the meat then season meat w/salt & pepper.
Combine egg w/ 3 tbsp. of the milk.
Put 1 1/2 cups of flour in pan & season w/ salt & pepper.
Coat steaks w/ flour, tap off any excess.
Drip steak in egg wash, coating both sides completely.
Coat steaks w/ flour on both sides again.
Fry steaks in the hot oil until brown on each side (about 3 minutes).
Remove from stove & drain on paper towels. Season w/ salt & pepper again.
Pour out most of the oil from the pan except about 1/4 cup.
Over medium heat, add 3 tbsp. flour & cook 3-4 minutes, whisking constantly.
Add rest of milk 1/2 cup at a time, still whisking constantly.
Bring to boil, reduce heat to medium-low. Season w/ salt & pepper.
Cook 8-10 minutes, whisking constantly. Gravy should be thick enough to coat back of a spoon.
Serve & enjoy!