This tart showcases the thyme flavoring of the goat cheese filling.
Preheat oven to 350 degrees, with rack on lowest shelf. In a medium bowl, toss leeks with oil, and season with salt and pepper. Set aside.
In a medium bowl, whisk together goat cheese, cream cheese, milk, 2 egg yolks, and thyme. Lightly season with salt and pepper. In a small bowl, beat remaining egg yolk with 1 tablespoon water, for egg wash.
Place pie crust on a rimmed baking sheet. Spread goat-cheese mixture on crust, leaving a 2-inch border. Top with leeks. Fold edge of dough over filling, pinching folds together to seal. Brush dough with egg wash.
Bake until crust is golden brown, about 1 hour. Let cool completely on a wire rack. Cut into wedges; serve.
Look for packages of store-bought pie dough in the refrigerator section of grocery stores. Do not use frozen pre-formed pie crusts.