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1
To make the crust, heat the butter in a small pot. Cook until the butter is lightly brown and has a nutty fragrance, 10 minutes. Stir in the water, sugar, and salt, and stir until dissolved.
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2
Remove the mixture from the heat, add the flour, and stir until the mixture comes together. Turn it out into a tart pan (or just onto a baking sheet, if you like), and lightly press. Let it cool for 5-10 minutes, until it's cool enough to handle.
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3
Press the crust into the pan until it's about 1/4? thick. Lightly score the base with a fork, and bake in a 400 degree oven until lightly browned, 12-15 minutes. Let cool completely.
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4
To make the peach compote, combine the peaches, honey, and vanilla in a small pot. Cook over low heat until the peaches have broken down completely, 10-15 minutes. Cool completely, then spread across the base of the cooled tart shell.
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5
To make the rice pudding filling, bring the rice, milk, cream, sugar, vanilla, and cinnamon to a boil over medium heat. Add the salt and egg yolk and whisk well to combine.
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6
Stir the mixture constantly over medium heat until the rice has absorbed the liquid and the mixture is thick and creamy, about 15-20 minutes.
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7
Transfer the mixture to a bowl, cover directly with plastic wrap, and refrigerate until cooled. When completely cool, pour into the cooled tart shell.
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8
To prepare the topping for the tart, prep the peaches and place on a baking sheet. In a small bowl, combine the sugar and cinnamon. Sprinkle the mixture into the center of each peach slice.
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9
Roast the peaches in a 400 degree oven until the sugar has caramelized and the peaches are soft, 7-10 minutes. Cool completely.
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10
Arrange the cooled peaches on top of the rice pudding filling, and top with toasted walnuts.
