Preheat your oven to 375°F (190°C) and generously grease a 9x13-inch baking dish with melted butter. Unroll the thawed phyllo dough and keep it covered with a slightly damp towel to prevent the delicate sheets from drying out.

In a large mixing bowl, whisk together the eggs and granulated sugar until the mixture is pale and slightly frothy, which takes about 2 minutes. Pour in the milk, vegetable oil, melted butter, vanilla extract, and baking powder, whisking until the liquid base is completely smooth.

Gently fold the ground walnuts into the liquid mixture. The resulting walnut custard will be slightly runny but heavily textured, which is the perfect consistency for soaking the pastry.

Lay two flat sheets of phyllo dough at the bottom of the prepared baking dish to create a sturdy base. Take the remaining phyllo sheets one by one, crumple them loosely into a ball like a piece of paper, and dip them briefly into the walnut mixture until coated.

Arrange the soaked, crumpled phyllo pieces side by side in the baking dish until the dish is fully packed. If you have any remaining walnut custard in the bowl, pour it evenly over the top of the assembled pastry to ensure maximum moisture.

Bake in the preheated oven for 40-45 minutes, or until the top is deeply golden brown and the center feels set when gently pressed. If the top begins to brown too quickly, cover the dish loosely with aluminum foil for the final 15 minutes of baking.

Remove the gužvara from the oven and let it cool in the pan for at least 20 minutes so the custard can fully set. Slice into squares and serve warm or at room temperature, ideally alongside a hot cup of coffee or tea.