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1
Quarter the plums, discard the pits, and cut into 1/2-inch pieces. Puree the plums in a food processor until smooth. Strain the puree through a medium-mesh sieve into a medium bowl, discarding the skins. There should be about 2 3/4 cups puree. Stir in the 1/2 cup sugar, the water, salt, and lemon juice. Taste for sweetness and add a little more sugar if necessary. Refrigerate for at least 2 hours or up to overnight. Churn in an ice cream machine according to the manufacturer's instructions. Freeze until scoopable, about 4 hours, depending on your freezer.
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2
Preheat the oven to 350u00b0F. Grease and flour a 9 1/2-inch springform pan. Tap out the excess flour.
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3
Sift the flour, baking powder, and cinnamon together in a bowl. Stir in the salt and the 1/2 cup cornmeal.
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4
In a bowl, cream the butter and sugar until light and fluffy. Add the eggs one at a time, beating well after each addition. In a small bowl, stir together the milk, lemon juice, and vanilla extract. In 3 additions, alternately stir in the dry ingredients and the milk into the butter mixture just until combined. Spread half of the batter in the prepared pan. Place half of the plums over the cake batter. Repeat with the remaining cake batter and remaining plums. Sprinkle the 1 tablespoon cornmeal over the top of the cake. Bake until a skewer inserted in the center comes out clean, about 50 minutes. Cool to room temperature.
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5
Cut the cake into slices. Place a slice on each plate with some plum sorbet. Serve immediately.
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6
The cake tastes best prepared the day you plan to serve it, but it can be made a day ahead. Store at room temperature, well wrapped in plastic wrap.
