Preheat the oven to 375 degrees F. Butter a 9-inch cake pan, then line the bottom with parchment paper and butter again. Dust the pan lightly with rice flour.
Spread the cooked rice along the bottom of the pan. Warm the milk in a small saucepan over low heat.
Beat the eggs, sugar, lemon zest and salt in a bowl with an electric mixer on medium until pale yellow and the eggs start to thicken, about 1 1/2 minutes, being careful not to overwhip which will cause the cake to rise and deflate when baked. Slowly stir about half the warm milk into the eggs to temper, then add all the eggs to the saucepan and heat, stirring constantly until it thickens slightly and almost coats the back of a spoon, 6 to 8 minutes.
Gently pour the custard over the rice and bake until the cake is just cooked through and wiggles only slightly in the very center, 40 to 50 minutes.
While the cake cooks, make the red wine cherry sauce. Combine the cherries, sugar and wine in a saucepan over medium heat. Cook, stirring, until the fruit softens and the liquid is reduced and syrupy, about 10 minutes. Cool and set aside.
Transfer the cake to a wire rack to cool for 30 minutes. Invert onto a platter and lift the pan. Remove the parchment paper. Cut into wedges and serve with the cherry sauce.
Alternatively, this cake can be baked in a gratin dish or square baking dish for a more casual rustic presentation with the sauce spooned over top.
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