Preheat the oven to 425 degrees F.
Combine 1/4 cup sugar and the cherries in a medium saucepan. Cook over medium-high heat, stirring often, until thick and syrupy, 15 to 18 minutes. Stir in the lemon juice and almond extract.
Stretch and pat the dough into a 10- to 11-inch round and put on a baking sheet. Brush with the butter and sprinkle with 1 tablespoon of the remaining sugar. Bake until golden brown all over, 10 to 12 minutes.
Spread the cherry compote on the pizza crust and sprinkle the chocolate chips over the top. Return to the oven to lightly melt the chocolate, about 1 minute. Whip the cream with the remaining tablespoon sugar until the cream is thick but does not hold a peak. Drizzle the sweetened cream over the pizza and sprinkle with grated chocolate if using. Cut into wedges and serve warm.
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