Preheat oven to 375 F.
In a large saucepan, melt 4 tbsp butter over low heat. Sprinkle with 1/2 cup flour and whisk for 1 minute until clumpy and combined.
Add 3/4 cup milk, a little at a time. Whisk until the consistency is like a thick cream.
Add crumbled feta, shredded cheddar, lightly beaten egg, salt, pepper, and chopped parsley. Stir until combined. Remove from heat and set aside to cool. Mixture will thicken as it cools.
Melt 3 tbsp butter in a microwave safe bowl and mix with 3 tbsp olive oil. Remove thawed phyllo dough from packaging and cover with a damp towel.
Working with 1 sheet at a time, lay a single phyllo sheet down on a large clean workspace. Using a pastry brush, paint the entire sheet with the butter/olive oil mixture until it looks soaked through.
Repeat with 3 more phyllo sheets, laying each one on top of the last one for a total of 4 sheets.
Using a sharp knife, cut diagonal slices to make 4 equal sized strips. Using a spoon, transfer a small dollop of the feta mixture to the bottom-center of one of the strips.
Starting at the bottom corner, fold into a triangle shape, enclosing the mixture. Continue to fold over and over until the final result is a triangle pouch. Repeat with the other 3 strips.
Place the cheese pie triangles on a baking sheet. Brush the tops with a little more butter/olive oil and sprinkle with sesame seeds. Bake at 375 F for 15-20 minutes or until golden-brown.