1. Preheat oven to 300 degrees. Sift together flour and salt into a medium bowl. Beat butter with a mixer on medium-high speed until fluffy, 3 to 5 minutes, scraping down sides of bowl with a rubber spatula as needed. Add sugar gradually, beating between additions; continue to beat until mixture is very pale, about 2 minutes total. Reduce speed to low, and add flour mixture; beat until just combined.

2. After beating in the flour, beat in 4 ounces chopped bittersweet chocolate (3/4 cup). Press dough evenly into a parchment-lined 9-by-13-inch rimmed baking sheet; refrigerate until firm, about 20 minutes. Cut dough in eighths lengthwise, then quarters crosswise, making 32 rectangles. Evenly pierce all over with a skewer.

3. Bake until shortbread is firm in center and golden brown, 50 minutes to 1 hour. Transfer pan to a wire rack; immediately recut rectangles with a paring knife. Let shortbread cool completely in pan.

4. Melt 5 ounces bittersweet chocolate. Dip bars into chocolate, place on parchment-lined baking sheet, and refrigerate until chocolate is set, about 10 minutes.