In a colander, toss eggplant with salt. Let stand and drain for 20 minutes. Rinse with cold water and set aside.
Heat oil in a large skillet over medium-high heat. Add eggplant and cook for 5 minutes, stirring often.
Add tomatoes and continue to cook and stir for another 5 minutes.
Add garlic, cumin, and water. Reduce heat and simmer, stirring occasionally, until eggplant is very tender, about 30 minutes.
Transfer to a bowl and stir in cheese. Cover and refrigerate overnight.
Preheat oven to 375°F. Line a baking sheet with parchment.
If using commercial phyllo, place two sheets on the counter and drizzle or smear with butter. Fold in half, then fold again.
If using homemade phyllo, place a sheet on the counter, smear with butter and fold over several time to form a square. Lightly roll the square thinner using a rolling pin.
Place a heaping tablespoon of filling in the center. Fold up the sides and lightly twist closed. Place on prepared baking sheet.
Bake for 25 to 35 minutes, or until golden brown. Remove from oven and let stand 5 minutes before serving.