French Silk Pie Bars

Name: French Silk Pie Bars
Ingredients: 8 Tbsp. (1 stick or 113 g) unsalted butter, cut into 16 pieces; 1½ cups (213 g) all-purpose flour, plus more for dusting; 1 tbsp. granulated sugar; ½ tsp. salt; 7 oz (200 g) bittersweet chocolate, melted and cooled; 4 large eggs, at room temperature; ¾ cup (150 g) granulated sugar; ¼ cup (50 g) packed brown sugar; ¼ tsp. salt; 3 Tbsp. water, at room temperature; 2 tsp. pure vanilla extract; 8 Tbsp. (1 stick or 113 g) unsalted butter, at room temperature, cut into 8 pieces; ½ cup (120 g) heavy cream; 4 oz (113 g) cream cheese, at room temperature; 2 Tbsp. granulated sugar; 1 tsp. pure vanilla extract; Pinch salt; 2 cups (480 g) heavy cream; 1 recipe Pie Dough Base, fully baked and cooled; Chocolate shavings, for decorating (optional)