Brush the olive oil onto a cookie sheet with no sides, or on the bottom of a jelly roll pan.
Combine the butter, flour, and salt in a food processor and pulse until a coarse meal is formed.
Add the water and process until the dough forms a ball.
Form the dough into a thick, flat disk, wrap in plastic wrap, and refrigerate for 30 minutes.
Roll out the dough directly on the oiled cookie sheet, forming a circle about 14 inches (35 cm) in diameter.
Combine the apples, honey, lemon juice, and thyme in a bowl and toss to combine well.
Arrange the apple slices on the pastry, leaving a 1 to 2 inch (3 to 5 cm) border all around.
Fold the border over the apples to form a rustic crust.
Pour any remaining honey-lemon juice mixture over the apples.
Bake in a preheated 400F (200C) oven for about 1 hour, until the crust is golden brown and the apples are tender.