Cheese Filling. Beat the eggs in a small bowl. Add the cheddar and feta cheeses and pepper to taste. Mix well. Use about 1 tablespoon of filling for each bureka. Dough. Preheat the oven to 350 degrees. Using a pastry brush, coat the bottom of a cookie sheet with some of the melted butter. Take a sheet of phyllo and cut lengthwise in strips, 4 1/2 inches wide. Butter the strips, fold over lengthwise, butter again, and place a tablespoon of filling on the end. Then fold up right to left as you would a flag, so that the end result is a plump triangle, buttering the outside at the end. Repeat with the remaining filling and dough. Beat the egg, brush the burekas with it, and sprinkle sesame seeds over the tops. Place on the cookie sheet and bake for 20 minutes or until golden in color. NOTE You can also mold and freeze the burekas after forming. Defrost for 2 hours and then bake. You can fill any leftover phyllo with chocolate chips or Nutella and make triangular treats. THREE WAYS TO FILL A BUREKA. Spinach Filling. Yield: About 2 cups, enough filling for about 20 burekas. 2 pounds fresh spinach or Swiss chard leaves, washed well, or two 10-ounce packages chopped frozen spinach. 2 large eggs, beaten lightly. 1/2 cup crumbled feta cheese. 1/2 cup grated cheddar cheese. 1/4 cup chopped fresh parsley. 2 tablespoons chopped fresh dill. 8 scallions, diced. Salt and freshly ground pepper to taste. Place the fresh spinach or Swiss chard leaves in a frying pan with only the water that clings to the leaves, and cook briefly until they wilt. (If using frozen spinach, simply defrost.) Drain very well, squeezing out as much of the water as possible. Cool and chop. Mix together the eggs, feta and cheddar cheeses, parsley, dill, and scallions. Add the spinach and salt and pepper to taste; mix well. Use about 1 tablespoon of filling for each bureka. Eggplant Filling. Yield: About 2 cups, enough filling for about 20 burekas. 2 medium eggplants (about 2 pounds). 1/3 cup kasseri or feta cheese, crumbled. 1/3 cup grated sheep or mozzarella cheese. 1/4 cup chopped fresh cilantro or parsley. Salt to taste. Preheat the oven to 450 degrees. Prick the skin of the eggplants all over and roast on an oiled cookie sheet for 25 minutes, turning occasionally. Remove the pulp from the skin, discarding the seeds and draining off any extra liquid. Cool slightly, then pat dry and coarsely chop. Combine the eggplant pulp, cheeses, and cilantro or parsley and mash well with a fork; add salt if needed. Use about 1 tablespoon of filling for each bureka. Cheese Filling. Yield: About 2 cups, enough filling for about 20 burekas. 2 large eggs. 1 cup grated cheddar cheese. 1 cup crumbled feta cheese. Freshly ground pepper to taste. Beat the eggs in a small bowl. Add the cheddar and feta cheeses and pepper to taste. Mix well. Use about 1 tablespoon of filling for each bureka. Other fillings: Spinach. Yield:About 2 cups, enough filling for about 20 burekas. 2 pounds fresh spinach or Swiss chard leaves, washed well, or two 10-ounce packages chopped frozen spinach. 2 large eggs, beaten lightly. 1/2 cup crumbled feta cheese. 1/2 cup grated cheddar cheese. 1/4 cup chopped fresh parsley. 2 tablespoons chopped fresh dill. 8 scallions, diced. Salt and freshly ground pepper to taste. Eggplant Filling. Yield: About 2 cups, enough filling for about 20 burekas. 2 medium eggplants (about 2 pounds). 1/3 cup kasseri or feta cheese, crumbled. 1/3 cup grated sheep or mozzarella cheese. 1/4 cup chopped fresh cilantro or parsley. Salt to taste. Joan Nathan shares her tips with Epicurious:  These pastries came to Israel with Sephardic Jews from Turkey and Greece. The first filling is more Greek-influenced, while the other two are more Turkish.  Nathan recommends a high-quality Greek feta cheese and a sharp cheddar for the fillings.  After folding up the burekas flag-style, be sure to pinch around the edges of each pastry to avoid filling spilling out during baking. Yield: About 60 bureka triangles.