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1
For the crostata: Preheat the oven to 375 degrees F. Place the pie crust on a parchment-lined baking sheet.
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2
Place a grill pan over medium-high heat or preheat a gas or charcoal grill.
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3
Drizzle the oil over the grill pan.
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4
Drizzle the peach halves with the balsamic vinegar, then grill flat-side down until softened and grill-marked, 3 to 4 minutes.
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5
Slice the peaches into wedges and arrange in a circle over the crust, leaving a 2-inch border.
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6
Fold the dough border over the filling to form an 8-inch round.
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7
Pleat the edge of the pastry and pinch to seal any cracks in the dough.
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8
Combine the sugar and 2 tablespoons water in a small saucepan and cook without stirring until it has become a deep amber color, about 5 minutes.
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9
Remove from the heat and slowly whisk in the butter, lemon juice and salt.
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10
Immediately pour the caramel over the peach slices.
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11
Bake the crostata until golden, 20 to 25 minutes.
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12
For the thyme whipped cream: Meanwhile, combine the heavy cream, sugar, vanilla and salt in the bowl of an electric mixer.
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13
Whip until the cream has soft peaks, about 2 minutes.
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14
Gently fold in the thyme.
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15
Let the crostata cool for 15 minutes to let the caramel settle, then cut into wedges and serve with a dollop of thyme whipped cream.