• 1 1/4 cups all-purpose flour , plus more for rolling dough
• 8 tablespoons (1 stick) unsalted butter , very cold, cut into 1/2-inch pieces
• 1/2 teaspoon salt
• 1 teaspoon sugar
• 2 to 3 tablespoons nonfat milk , very cold

• 7 tablespoons unsalted butter
• 7 to 8 Granny Smith apples , peeled, cored and quartered
• 1/2 cup sugar
• 4 sprigs lavender
• 1/2 cup creme fraiche (optional)
• 1/2 cup sour cream mixed with 1 tablespoon brown sugar (optional)

To make crust: In a food processor, combine flour, butter, salt and sugar; pulse 6 to 8 times, until mixture resembles coarse meal. Add milk 1 tablespoon at a time, pulsing until mixture solidifies into a ball. Remove dough from machine and shape into a 5-inch disc; wrap in plastic wrap and refrigerate at least 1 hour.

Place a sheet of parchment paper on a floured board, and allow dough to stand, unwrapped, until just pliable, about 10 minutes. With a floured rolling pin, roll out dough into an 11-inch circle. Move dough a quarter turn with every roll, making sure it is not sticking to the paper underneath; dough should be 1/4 to 1/8 inch thick. Transfer dough, on parchment paper, back into the refrigerator; let chill while preparing filling.

To make filling: Preheat oven to 425°. In a deep 12-inch skillet, melt butter over medium-high heat. Stir in apples, sugar and lavender. Cook, stirring occasionally so apples and sugar don't stick, about 20 minutes. Increase heat to high and cook until apples are a deep golden brown, 12 to 15 minutes. Shake pan to make sure sugar isn't burning; the color should be a very deep brown.

To a 10-inch glass pie dish add apple mixture, discarding lavender sprigs. Place rolled dough on top of apples; tuck edges of dough around apples on the inside of pie dish. Place in center of oven and bake until pastry turns golden brown, 35 to 40 minutes. Remove tart from oven and immediately place a large, heatproof serving platter or board on top of pie dish; flip over and give a firm tap to release any apples that may be stuck to bottom. Slowly raise pie dish. Serve tart warm or at room temperature. Serve with crème fraîche or sour cream mixed with brown sugar, if desired.