Lightly brush 4 sheets of phyllo dough with oil and layer them in a medium baking pan. Sprinkle a little of the cheese mixture on top. Continue layering phyllo and cheese alternately, finishing with the last 2 sheets of phyllo on top.

In a bowl, whisk together the milk, eggs, and heavy cream just until combined—do not overmix, so the mixture stays pourable and can soak into the phyllo.

Score the pie into pieces, cutting almost to the bottom but not all the way through. Pour the milk mixture evenly over the top.

Bake in a preheated oven until the pie is golden brown and cooked through.