Thaw the shredded phyllo strands.
Preheat the oven to 190°C/375°F.
Over low heat, melt the butter in a small saucepan, add oil, stir well and set aside.
Lightly, pull the shredded phyllo dough (kataifi) with your hands to separate into a loose pile.
Pour the melted butter-oil mixture over the shredded dough and mix well to infuse the butter equally with the dough.
Brush the muffin tin with some melted butter.
Take a small piece of the shredded kataifi dough, about 15 cm/6 inches long and 3cm/ about 1 inch wide, fold inwards of the sides to shape it a small round circle large enough to fit the bottom and part of the sides of the muffin tin. With your thumb, press the pastry to fit well. Divide the rest of the shredded phyllo dough among the muffin tin.
Bake to a golden brown color about 10-12 minutes. Remove from the oven and set aside to cool down.