Melt the 6 tablespoons butter in a large saucepan.
Whisk in the flour and cook slightly (1-2 minutes) to get rid of 'raw' flour taste.
Slowly whisk in the milk.
Cook over medium heat, whisking constantly, until sauce thickens.
Remove from heat and let cool for 10 minutes.
Quickly whisk the eggs into the sauce one at a time.
Then stir in the cheese.
Preheat oven to 375°F.
Butter a 13 X 9" Pyrex baking dish generously (you can also use a larger baking pan - the tiropita just comes out a little thinner, but is nicer for appetizer servings).
Flatten phyllo dough and cover with a sheet of wax paper and a lightly dampened towel (to avoid drying out).
Take one sheet at a time and place in baking dish.
Brush phyllo generously with butter.
Use about 6 sheets this way and then add 1/2 of cheese filling.
Layer 3 more sheets of phyllo (brushing each one with butter) and then top with remaining cheese filling.
Finally, layer 6 sheets of phyllo over top (brushing each one with butter) and fold in the edges to make the tiropita look neat.
Brush top generously with remaining butter.
Score top of phyllo carefully with the point of a sharp knife, just cutting through pastry (only cut through the top layers of pastry, do not cut all the way down to the bottom layer), into the size of pieces you will want to serve.
Make sure you don't cut right through pie.
Bake for about 45 minutes to one hour, or until golden brown.
(Make sure bottom crust is nice and golden- if it isn't- put it directly on floor of oven for about 10 minutes to brown faster. You don't want a soggy, uncooked bottom pastry).
Variation: I often add 8 oz. of a good-quality, chopped, smoked ham to the cheese filling.