In a bowl, combine the flour, diced butter, egg, oil and water. Season with salt and pepper. Knead by had until dough becomes flexible and elastic. Place in the fridge for an hour.
In a bowl, stir together goat cheese, honey and walnuts. Add a little bit of thyme and pepper
Preheat oven to 450F
Roll out the dough on a floured surface. Using a glass or pastry cutter, cut the dough into several rounds. Place a tsp of filling in the middle of the circle, close the turnovers and seal them by pressing around the edges.
Whisk the egg yolk with one tbsp of water and brush the turnovers with the egg yolk. Bake for 20 to 25 minutes.