Preheat the oven to 350°F and grease and flour an 11x7-inch pan (a 9x9-inch pan may be used but will require longer baking).
In a 2‑quart saucepan over low heat, combine 1/2 cup (1 stick) salted butter and 10 ounces white vanilla baking chips, stirring frequently until melted and smooth; remove from heat and allow to cool slightly.
Stir in 3/4 cup granulated sugar, 3 large eggs, 1 teaspoon vanilla extract, the seeds from 1/2 vanilla bean, 1 1/4 cups all-purpose flour, and 1/4 teaspoon salt until well combined.
Spread the batter evenly into the prepared pan.
Bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean; remove from the oven and cool completely in the pan.
Run a knife around the pan edges and invert the slab onto a cutting board, then turn upright so the unglazed side is down and the top is exposed.
Make the glaze: in a medium bowl, beat 1 1/2 cups powdered sugar with 3 tablespoons room-temperature salted butter and 1/2 teaspoon vanilla extract, adding 1 to 2 tablespoons milk or cream as needed to reach a smooth, spreadable consistency.
Spread the glaze evenly over the cooled bars and allow it to set; optionally drizzle with melted chocolate (see notes) for decoration.
Chill briefly if desired, then cut into 25 bars and serve.