Mix the feta, mozzarella, egg yolk, parsley and ground black pepper in a bowl.
Combine the white and black sesame seeds in a bowl. Set aside.
Lay 3 sheets of phyllo on a work surface, keeping the remaining sheets covered with a well wrung out, moist paper towel or kitchen towel. Cut the long width of phyllo in half, forming 2 rectangles.
Spoon 2 oz. of filling along the short edge of the phyllo. Roll the phyllo over the cheese mixture while compressing it to stay in place. Roll once, then fold the outer edges like a burrito. Continue rolling the phyllo. About 2” from the top, make two cuts to create a point. Wet the point of the phyllo with water and firmly roll to seal. Keep covered until all rectangles are filled and rolled.
In a large skillet, add about 1” of oil. Heat on medium heat to 325°F. Gently lower the cigars, working in batches, into the oil, leaving enough room to roll the cigars to brown on all sides.
Fry until crispy and light golden brown on all sides.
Remove from the oil onto a plate lined with paper towels. Immediately sprinkle with sesame seeds and kosher salt.