For the Basil Cream
- 3/4 cup heavy cream
- 1/3 cup loosely packed fresh basil, chopped
- 2 tablespoons sugar
- 3/4 cup mascarpone cheese
For the Fried Basil
- 2 cups vegetable oil
- 18 to 24 large fresh basil leaves
- Sugar, for sprinkling
For the Dough
- 2 1/2 cups all-purpose flour, plus more for surface
- 1 1/8 teaspoon salt
- 1 teaspoon sugar
- 8 ounces (1 cup) cold unsalted butter, cut into small pieces
- 1/3 cup plus 2 tablespoons ice water
For the Galette
- 1 pound strawberries, hulled
- 1/4 cup plus 1 tablespoon sugar
- 2 teaspoons cornstarch
- 1 large egg yolk
- 1 tablespoon water
- 1 tablespoon cold unsalted butter, cut into small pieces
- Make the basil cream: Combine cream, basil, and sugar in a heatproof bowl. Set bowl over a small saucepan of simmering water, and stir until sugar dissolves, about 4 minutes. Cover with plastic wrap, and refrigerate for at least 1 hour (or up to 2 hours for a more pronounced basil flavor). Strain through a fine sieve into a bowl. Add mascarpone, and whisk until medium peaks form. Cover, and refrigerate until ready to serve, up to 2 hours.
- Make the fried basil: Heat oil in a deep skillet to 325 degrees. Fry basil, a few leaves at a time, for 12 seconds. (The leaves will cause the hot oil to spatter; step away from the pan while they cook.) Drain leaves on paper towels, and let cool completely. Sprinkle both sides of the leaves with sugar. (Basil can be stored at room temperature overnight.)
- Make the dough: Pulse flour, salt, and sugar in a food processor to combine. Add butter, and pulse until mixture forms coarse crumbs. Add ice water, and pulse until just combined (dough will still be crumbly). Shape dough into a disk, wrap in plastic, and refrigerate for at least 1 hour (or overnight).
- Preheat oven to 350 degrees. On a floured surface, roll dough to 1/4 inch thickness. Cut out a 10-inch round, and transfer to a parchment-lined rimmed baking sheet. Refrigerate for 30 minutes.
- Make the galette: Cut strawberries lengthwise into 1/4-inch-thick slices. Reserve end pieces for another use. Toss slices with 1/4 cup sugar and the cornstarch, and immediately arrange them in concentric circles on dough. Start 1 inch from edge, overlapping slices slightly. Fold edge of dough over berries. Refrigerate for 15 minutes.
- Whisk together yolk and water. Brush dough with the egg wash, and sprinkle with remaining 1 tablespoon sugar. Dot berries with butter. Bake until crust is golden brown, 40 to 45 minutes.
- Transfer to a serving plate. Serve warm with basil cream and fried basil.
Both the basil cream and sugared leaves can be prepared ahead.