How to Make It
Preheat oven to 375°F. Combine prunes and 1/3 cup water in small saucepan and bring to a boil. Reduce heat to low, cover, and simmer until soft, 8 to 10 minutes.
Transfer mixture to food processor and add ginger, lemon zest, lemon juice, and a pinch of salt. Process until smooth.
Unroll the crescent roll dough on a lightly-floured piece of parchment paper and separate into triangles. Gently stretch each one so that all sides are about the same length. Spread a scant tablespoon of filling on each one, leaving a ¼” border. Fold each triangle in half, long end to long end, aligning to seal. Crimp the edges with a fork, and cut vents with a sharp paring knife on the top. Brush with beaten egg.
Transfer parchment paper to a baking sheet and bake until golden brown, 14 to 16 minutes.
Prepare the glaze: Melt butter in a small skillet until it foams and begins to brown, 1 to 2 minutes. Transfer to a small bowl and add the cream cheese, whisking until smooth. Add powdered sugar, 1 tablespoon milk, and a pinch of salt and whisk to combine. Add additional tablespoon of milk to thin out glaze if necessary. Drizzle over baked turnovers. Serve warm.