Preheat oven to 350.
Lightly grease a 12x9 rectangular baking dish; set aside.
In a large mixing bowl, combine eggs, milk, cottage cheese, cream cheese, feta cheese, oil, thyme leaves, salt and pepper.
Whisk the mixture until thoroughly combined. Mixture will be runny.
Spread 1/4 cup of egg mixture onto the bottom of previously prepared baking dish.
Place 1 phyllo sheet over the mixture. (Cut phyllo sheets to fit the baking dish.)
Brush it with melted butter.
Layer two more phyllo sheets, brushing each sheet with melted butter before adding the next.
Ladle 1/4 of feta/egg mixture over phyllo sheets.
As you work, keep the unused stack of phyllo sheets covered so they don't dry up.
Stack 3 more phyllo sheets, brushing each sheet with melted butter before adding the next, and cover with 1/4 of the egg mixture.
Continue the process until all ingredients are used up, ending with egg mixture on top.
Bake for 1 hour. Casserole will be browned and puffed up.
Lower oven temperature to 250 and continue to bake for 30 minutes, or until custard is baked and set.
Let cool at least 30 minutes before cutting.
Cut into bars.
Serve warm or cold.