Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x9-inch baking pan.

Melt together white chocolate and butter in the top of a double boiler over barely simmering water; stir occasionally until smooth. Set aside to cool.

Combine flour and salt in a medium bowl; set aside.

Beat eggs in a large bowl with an electric mixer until foamy. Gradually add sugar and vanilla with the mixer still running. Drizzle in white chocolate mixture; mix well. Stir in flour mixture with a rubber spatula or wooden spoon. Fold in chocolate chips. Spread batter evenly into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the middle comes out clean, about 25 minutes. Cool in the pan on a wire rack before cutting into bars.