Prepare the Filling:

In a medium bowl, combine the feta cheese, ricotta cheese, grated Parmesan cheese, beaten egg, dill (if using), parsley, salt, and pepper. Mix until well combined and set aside.

Prepare the Phyllo Dough:

Preheat your oven to 350°F (175°C).
Lay out one sheet of phyllo dough on a clean, flat surface. Keep the remaining sheets covered with a damp towel to prevent them from drying out.
Brush the phyllo sheet lightly with the melted butter and olive oil mixture.
Place another sheet of phyllo on top and brush again with the butter mixture. Repeat this process with a total of 3-4 sheets.

Assemble the Tyropitakia:

Cut the layered phyllo sheets into strips about 3 inches wide.
Place a tablespoon of the cheese filling at one end of each strip.
Fold the end of the strip over the filling to form a triangle. Continue folding the strip, maintaining the triangular shape, until you reach the end of the strip.
Repeat the process with the remaining phyllo sheets and filling.

Bake the Tyropitakia:

Place the triangles on a baking sheet lined with parchment paper. Brush the tops with the remaining butter and olive oil mixture.
Bake in the preheated oven for 20-25 minutes, or until the triangles are golden brown and crispy.

Serve:

Let the tyropitakia cool slightly before serving. They are best enjoyed warm but can also be served at room temperature.